SlideShare a Scribd company logo
1 of 22
YES-NO-STAND-UP Game
Questions:
1. Do you like chocolates?
2. Do you like to hurt
people?
3. Do you love math?
4. Is 2 + 2 = 5?
5. Is 9= 3 ?
6. Is 4 a perfect square?
7. Is 1 x 2 = 3?
8. Is 100 not a perfect
square?
9. Is there a way to predict
the nature of the root?
10. Are you familiar with
discriminant in a quadratic?
equation?
NATURE OF ROOTS OF
QUADRATIC EQUATION
At the end of this lesson, the students are expected to:
Objectives
b. describes the nature of roots of a quadratic
equation through its discriminant;
c. value the importance of discriminant through the
roots of the quadratic equation.
a. identifies the nature of roots of a given quadratic
equation;
Group Activity
1. 𝒙𝟐
+ 𝟒𝒙 + 𝟑 = 𝟎 2. 𝒙𝟐
− 𝟏 = 𝟎
Boys vs. Girls
Direction: Find the roots of the quadratic eaquation
using quadratic formula. Boys group will answer #1 and
girls group will answer the #2. The groups have 5
minutes to answer and choose a representative to
present their answer.
Questions from the activity:
1. What is the standard form of the quadratic equation?
2. What is the formula for quadratic formula?
3. What is the formula of a discriminant?
4. Why do we need to determine the discriminant
of the quadratic equation?
WHY USE THE QUADRATIC FORMULA?
 The quadratic formula allows you to solve ANY quadratic
equation, even if you cannot factor it.
 An important piece of the quadratic formula is what’s under the radical:
b2 – 4ac
 This piece is called the discriminant.
WHY IS THE DISCRIMINANT IMPORTANT?
The value of the expression 𝒃𝟐
– 4ac is
called the discriminant of the quadratic
equation ax² + bx + c = 0. This value can be
used to describe the nature of the roots
of a quadratic equation. It can be zero,
positive and perfect square, positive but
not perfect square or negative.
???
Nature of Roots of Quadratic Equation
Discriminant
• It is the number being
used to describe the
nature of roots of a
quadratic equation.
Formula:
d = b2 – 4ac
provided that the
equation is in standard
form.
discriminant Nature of Roots
d = 0
real numbers and equal
roots
d > 0
d is a perfect
square
rational numbers and
unequal roots
d is not a
perfect
square
irrational numbers and
unequal roots
d < 0 No real roots
9
Remember: Equation must be in standard form Example 1: Describe the nature of roots
of 3t2 + 5t = 2
Solution:
3t2 + 5t = 2
Step 1: Write first the equation into
standard form: 3t2 + 5t – 2 = 0
Step 2: Identify a, b and c
a = 3, b = 5, c = –2
Step 3: Substitute these values to
d = b2 – 4ac
d = (5)2 – 4(3)(–2)
d = 25 + 24
d = 49
Nature of Roots:
rational numbers and equal
discriminant Nature of Roots
d = 0
real numbers and equal
roots
d > 0
d is a perfect
square
rational and unequal roots
d is not a
perfect
square
irrational and unequal roots
d < 0 No real root
Remember: Equation must be in standard form Example 2: Compute for the discriminant
of (x – 2)2 = 0
Solution:
Step 1: Write first the equation into
standard form: x2 – 4x + 4 = 0
Step 2: Identify a, b and c
a = 1, b = –4, c = 4
Step 3: Substitute these values to
d = b2 – 4ac
d = (–4)2 – 4(1)(4)
d = 16 – 16
d = 0
Nature of Roots:
real numbers and equal
discriminant Nature of Roots
d = 0 real numbers and equal
d > 0
d is a
perfect
square
rational numbers and
unequal
d is not a
perfect
square
irrational numbers and
unequal
d < 0 No real roots
Remember: Equation must be in standard form Example 3: What is the nature of roots of
h2 – 16 = – 3h
Solution:
Step 1: Write first the equation into
standard form: h2 + 3h – 16 = 0
Step 2: Identify a, b and c
a = 1, b = 3, c = –16
Step 3: Substitute these values to
d = b2 – 4ac
d = (3)2 – 4(1)(–16)
d = 9 + 64
d = 73
Nature of Roots:
irrational numbers and unequal
discriminant Nature of Roots
d = 0 real numbers and equal
d > 0
d is a
perfect
square
rational numbers and
unequal
d is not a
perfect
square
irrational numbers and
unequal
d < 0 No real roots
Remember: Equation must be in standard form Example 4: Describe the nature of roots
of the equation k2 - 3k = - 6
Solution:
Step 1: Write first the equation into
standard form: k2 - 3k + 6 = 0
Step 2: Identify a, b and c
a = 1, b = -3, c = 6
Step 3: Substitute these values to
d = b2 – 4ac
d = (-3)2 – 4(1)(6)
d = 9 – 24
d = – 15
Nature of Roots:
No real roots
discriminant Nature of Roots
d > 0
d is a
perfect
square
• Two real, rational and
unequal roots
d is not a
perfect
square
• Two real, irrational and
unequal roots
d = 0 • One real and rational root.
d < 0 • No real root
discriminant Nature of Roots
d = 0 real numbers and equal
d > 0
d is a
perfect
square
rational numbers and
unequal roots
d is not a
perfect
square
irrational numbers and
unequal roots
d < 0 No real root
Remember: Equation must be in standard form Example 5: Determine the nature of roots
of the equation 3x2 + 11x + 8 = 0
Solution:
Step 1: Write first the equation into
standard form: 3x2 + 11x + 8 = 0
Step 2: Identify a, b and c
a = 3, b = 11, c = 8
Step 3: Substitute these values to
d = b2 – 4ac
d = (11)2 – 4(3)(8)
d = 121 – 96
d = 25
Nature of Roots:
rational numbers and unequal
discriminant Nature of Roots
d = 0 real numbers and equal
d > 0
d is a
perfect
square
rational numbers and
unequal roots
d is not a
perfect
square
irrational and unequal
roots
d < 0 No real root
Activity
Place Me on the Table!
Direction: Answer the following.
1. Complete the table below.
Equation b²-4ac Nature of roots
1. x² + 5x + 4 = 0
2. 2x² + x - 21= 0
3. 4x² +4x + 1 = 0
4. x² - 2x - 2 = 0
5. 9x² + 16= 0
2. How would you describe the roots of
quadratic equation when the value of b²-
4ac is 0? Positive and Perfect Square?
Positive but not Perfect Square? Negative?
.
3. Which quadratic equation has
roots that are real numbers and
equal? Rational numbers? Irrational
numbers? Not real numbers?
4. How do you determine the
quadratic equation having roots that
are real numbers and equal?
Rational numbers? Irrational
numbers? Not real numbers?
Directions: Determine the discriminants and nature of the roots of the following
quadratic equations. Write your answer on the space provided.
Evaluation
2. 𝑥2
+ 9𝑥 + 20 = 0
1. 𝑥2 + 6𝑥 + 9 = 0
3. 2𝑥2 − 10𝑥 + 8 = 0
4. 𝑥2 + 5𝑥 + 10 = 0
5. 𝑥2
+ 6𝑥 + 3 = 0
discriminant:
discriminant:
discriminant:
discriminant:
discriminant: nature of the roots
nature of the roots
nature of the roots
nature of the roots
nature of the roots
Assignment:
Study Sum and Product of Roots of a
Quadratic Equation.
Activity
Thank you.
Nature_of_Roots_of_Quadratic_Equation.pptx
Nature_of_Roots_of_Quadratic_Equation.pptx
Nature_of_Roots_of_Quadratic_Equation.pptx

More Related Content

What's hot

Lesson Plan for Quadrilateral.docx
Lesson Plan for Quadrilateral.docxLesson Plan for Quadrilateral.docx
Lesson Plan for Quadrilateral.docxXyza4
 
MATH-8 WEEKS 8 Q3 .pptx
MATH-8 WEEKS 8 Q3 .pptxMATH-8 WEEKS 8 Q3 .pptx
MATH-8 WEEKS 8 Q3 .pptxlarryazarias
 
Mathematics 9 Lesson 4-C: Joint and Combined Variation
Mathematics 9 Lesson 4-C: Joint and Combined VariationMathematics 9 Lesson 4-C: Joint and Combined Variation
Mathematics 9 Lesson 4-C: Joint and Combined VariationJuan Miguel Palero
 
Quadrilateral that are parallelogram.pptx
Quadrilateral that are parallelogram.pptxQuadrilateral that are parallelogram.pptx
Quadrilateral that are parallelogram.pptxRizaCatli2
 
Math 7 – adding and subtracting polynomials
Math 7 – adding and subtracting polynomialsMath 7 – adding and subtracting polynomials
Math 7 – adding and subtracting polynomialsRebekah Andrea Fullido
 
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...AngelaCamillePaynant
 
Lesson 1.9 a adding and subtracting rational numbers
Lesson 1.9 a   adding and subtracting rational numbersLesson 1.9 a   adding and subtracting rational numbers
Lesson 1.9 a adding and subtracting rational numbersJohnnyBallecer
 
Lesson plan on Mean for Ungrouped Data
Lesson plan on Mean for Ungrouped DataLesson plan on Mean for Ungrouped Data
Lesson plan on Mean for Ungrouped DataLorie Jane Letada
 
Math10 curriculum map docx
Math10 curriculum map docxMath10 curriculum map docx
Math10 curriculum map docxEmaEmitsCP
 
DLL_ENGLISH 5_Q4_W1.docx
DLL_ENGLISH 5_Q4_W1.docxDLL_ENGLISH 5_Q4_W1.docx
DLL_ENGLISH 5_Q4_W1.docxMONMONMAMON
 

What's hot (20)

Mathematics 9 Variations
Mathematics 9 VariationsMathematics 9 Variations
Mathematics 9 Variations
 
Lesson Plan for Quadrilateral.docx
Lesson Plan for Quadrilateral.docxLesson Plan for Quadrilateral.docx
Lesson Plan for Quadrilateral.docx
 
MATH-8 WEEKS 8 Q3 .pptx
MATH-8 WEEKS 8 Q3 .pptxMATH-8 WEEKS 8 Q3 .pptx
MATH-8 WEEKS 8 Q3 .pptx
 
Mathematics 9 Lesson 4-C: Joint and Combined Variation
Mathematics 9 Lesson 4-C: Joint and Combined VariationMathematics 9 Lesson 4-C: Joint and Combined Variation
Mathematics 9 Lesson 4-C: Joint and Combined Variation
 
Quadrilateral that are parallelogram.pptx
Quadrilateral that are parallelogram.pptxQuadrilateral that are parallelogram.pptx
Quadrilateral that are parallelogram.pptx
 
Math 7 – adding and subtracting polynomials
Math 7 – adding and subtracting polynomialsMath 7 – adding and subtracting polynomials
Math 7 – adding and subtracting polynomials
 
A detailed lesson plan in permutation
A detailed lesson plan in permutationA detailed lesson plan in permutation
A detailed lesson plan in permutation
 
Theorems on kite
Theorems on kiteTheorems on kite
Theorems on kite
 
Lp (similar polygons)
Lp (similar polygons)Lp (similar polygons)
Lp (similar polygons)
 
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
3-MATH 8-Q3-WEEK 2-ILLUSTRATING TRIANGLE CONGRUENCE AND Illustrating SSS, SAS...
 
Division Of Polynomials
Division Of PolynomialsDivision Of Polynomials
Division Of Polynomials
 
Integers and Operation of Integers
Integers and Operation of IntegersIntegers and Operation of Integers
Integers and Operation of Integers
 
detailed-lesson-plan-math-9.pdf
detailed-lesson-plan-math-9.pdfdetailed-lesson-plan-math-9.pdf
detailed-lesson-plan-math-9.pdf
 
Lesson 1.9 a adding and subtracting rational numbers
Lesson 1.9 a   adding and subtracting rational numbersLesson 1.9 a   adding and subtracting rational numbers
Lesson 1.9 a adding and subtracting rational numbers
 
Slope lesson plan
Slope lesson planSlope lesson plan
Slope lesson plan
 
Math 9 similar triangles intro
Math 9   similar triangles introMath 9   similar triangles intro
Math 9 similar triangles intro
 
Combined Variation
Combined  VariationCombined  Variation
Combined Variation
 
Lesson plan on Mean for Ungrouped Data
Lesson plan on Mean for Ungrouped DataLesson plan on Mean for Ungrouped Data
Lesson plan on Mean for Ungrouped Data
 
Math10 curriculum map docx
Math10 curriculum map docxMath10 curriculum map docx
Math10 curriculum map docx
 
DLL_ENGLISH 5_Q4_W1.docx
DLL_ENGLISH 5_Q4_W1.docxDLL_ENGLISH 5_Q4_W1.docx
DLL_ENGLISH 5_Q4_W1.docx
 

Similar to Nature_of_Roots_of_Quadratic_Equation.pptx

Nature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptxNature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptxssuser2b0f3a
 
Strategic intervention material discriminant and nature of the roots
Strategic intervention material discriminant and nature of the rootsStrategic intervention material discriminant and nature of the roots
Strategic intervention material discriminant and nature of the rootsmaricel mas
 
COT 23-24.pptxDDfovhasdp9ouifn[douinas[dovnas0dunadin
COT 23-24.pptxDDfovhasdp9ouifn[douinas[dovnas0dunadinCOT 23-24.pptxDDfovhasdp9ouifn[douinas[dovnas0dunadin
COT 23-24.pptxDDfovhasdp9ouifn[douinas[dovnas0dunadinjanianfuna1
 
Nature of the roots and sum and product of the roots of a quadratic equation
Nature of the roots and sum and product of the roots of a quadratic equationNature of the roots and sum and product of the roots of a quadratic equation
Nature of the roots and sum and product of the roots of a quadratic equationCipriano De Leon
 
Grade 9: Mathematics Unit 1 Quadratic Equations and Inequalities.
Grade 9: Mathematics Unit 1 Quadratic Equations and Inequalities.Grade 9: Mathematics Unit 1 Quadratic Equations and Inequalities.
Grade 9: Mathematics Unit 1 Quadratic Equations and Inequalities.Paolo Dagaojes
 
The-Nature-of-the-Roots (1).pptx
The-Nature-of-the-Roots (1).pptxThe-Nature-of-the-Roots (1).pptx
The-Nature-of-the-Roots (1).pptxKurtDelaPena
 
410629531-G9-WEEK-3 dll.doc
410629531-G9-WEEK-3 dll.doc410629531-G9-WEEK-3 dll.doc
410629531-G9-WEEK-3 dll.docJosephSPalileoJr
 
quadraticequations-111211090004-phpapp02.pptx
quadraticequations-111211090004-phpapp02.pptxquadraticequations-111211090004-phpapp02.pptx
quadraticequations-111211090004-phpapp02.pptxanithanatarajan15
 
6th grade math review worksheet(1)
6th grade math review worksheet(1)  6th grade math review worksheet(1)
6th grade math review worksheet(1) dihelp2learn
 
Page 1 of 5I have completed this assignment myself; working in.docx
Page 1 of 5I have completed this assignment myself; working in.docxPage 1 of 5I have completed this assignment myself; working in.docx
Page 1 of 5I have completed this assignment myself; working in.docxbunyansaturnina
 
Math 7 lesson 9 division of integers
Math 7   lesson 9 division of integersMath 7   lesson 9 division of integers
Math 7 lesson 9 division of integersAriel Gilbuena
 
nature of the roots and discriminant
nature of the roots and discriminantnature of the roots and discriminant
nature of the roots and discriminantmaricel mas
 
sim2-151007132331-lva1-app6892.pdf
sim2-151007132331-lva1-app6892.pdfsim2-151007132331-lva1-app6892.pdf
sim2-151007132331-lva1-app6892.pdfJenniferABagol
 
Mathematics 9 Quadratic Equations and Inequalities
Mathematics 9 Quadratic Equations and InequalitiesMathematics 9 Quadratic Equations and Inequalities
Mathematics 9 Quadratic Equations and InequalitiesJuan Miguel Palero
 
Math module (unit 1)
Math module (unit 1)Math module (unit 1)
Math module (unit 1)M.J. Labrador
 

Similar to Nature_of_Roots_of_Quadratic_Equation.pptx (20)

Nature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptxNature of Roots of Quadratic Equation.pptx
Nature of Roots of Quadratic Equation.pptx
 
Strategic intervention material discriminant and nature of the roots
Strategic intervention material discriminant and nature of the rootsStrategic intervention material discriminant and nature of the roots
Strategic intervention material discriminant and nature of the roots
 
COT 23-24.pptxDDfovhasdp9ouifn[douinas[dovnas0dunadin
COT 23-24.pptxDDfovhasdp9ouifn[douinas[dovnas0dunadinCOT 23-24.pptxDDfovhasdp9ouifn[douinas[dovnas0dunadin
COT 23-24.pptxDDfovhasdp9ouifn[douinas[dovnas0dunadin
 
Nature of the roots and sum and product of the roots of a quadratic equation
Nature of the roots and sum and product of the roots of a quadratic equationNature of the roots and sum and product of the roots of a quadratic equation
Nature of the roots and sum and product of the roots of a quadratic equation
 
L1 Quadratic Equations.pptx
L1 Quadratic Equations.pptxL1 Quadratic Equations.pptx
L1 Quadratic Equations.pptx
 
Grade 9: Mathematics Unit 1 Quadratic Equations and Inequalities.
Grade 9: Mathematics Unit 1 Quadratic Equations and Inequalities.Grade 9: Mathematics Unit 1 Quadratic Equations and Inequalities.
Grade 9: Mathematics Unit 1 Quadratic Equations and Inequalities.
 
The-Nature-of-the-Roots (1).pptx
The-Nature-of-the-Roots (1).pptxThe-Nature-of-the-Roots (1).pptx
The-Nature-of-the-Roots (1).pptx
 
410629531-G9-WEEK-3 dll.doc
410629531-G9-WEEK-3 dll.doc410629531-G9-WEEK-3 dll.doc
410629531-G9-WEEK-3 dll.doc
 
Dll wk-1-lc-1
Dll wk-1-lc-1Dll wk-1-lc-1
Dll wk-1-lc-1
 
Dll wk-1-lc-1
Dll wk-1-lc-1Dll wk-1-lc-1
Dll wk-1-lc-1
 
discriminant.pptx
discriminant.pptxdiscriminant.pptx
discriminant.pptx
 
quadraticequations-111211090004-phpapp02.pptx
quadraticequations-111211090004-phpapp02.pptxquadraticequations-111211090004-phpapp02.pptx
quadraticequations-111211090004-phpapp02.pptx
 
6th grade math review worksheet(1)
6th grade math review worksheet(1)  6th grade math review worksheet(1)
6th grade math review worksheet(1)
 
Page 1 of 5I have completed this assignment myself; working in.docx
Page 1 of 5I have completed this assignment myself; working in.docxPage 1 of 5I have completed this assignment myself; working in.docx
Page 1 of 5I have completed this assignment myself; working in.docx
 
Math 7 lesson 9 division of integers
Math 7   lesson 9 division of integersMath 7   lesson 9 division of integers
Math 7 lesson 9 division of integers
 
nature of the roots and discriminant
nature of the roots and discriminantnature of the roots and discriminant
nature of the roots and discriminant
 
sim2-151007132331-lva1-app6892.pdf
sim2-151007132331-lva1-app6892.pdfsim2-151007132331-lva1-app6892.pdf
sim2-151007132331-lva1-app6892.pdf
 
Mathematics 9 Quadratic Equations and Inequalities
Mathematics 9 Quadratic Equations and InequalitiesMathematics 9 Quadratic Equations and Inequalities
Mathematics 9 Quadratic Equations and Inequalities
 
Math module (unit 1)
Math module (unit 1)Math module (unit 1)
Math module (unit 1)
 
Math 9 (module 1)
Math 9 (module 1)Math 9 (module 1)
Math 9 (module 1)
 

Recently uploaded

Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management SystemChristalin Nelson
 
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17Celine George
 
The State of AI in Insights and Research 2024: Results and Findings
The State of AI in Insights and Research 2024: Results and FindingsThe State of AI in Insights and Research 2024: Results and Findings
The State of AI in Insights and Research 2024: Results and FindingsRay Poynter
 
Oppenheimer Film Discussion for Philosophy and Film
Oppenheimer Film Discussion for Philosophy and FilmOppenheimer Film Discussion for Philosophy and Film
Oppenheimer Film Discussion for Philosophy and FilmStan Meyer
 
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxMULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxAnupkumar Sharma
 
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONTHEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONHumphrey A Beña
 
Textual Evidence in Reading and Writing of SHS
Textual Evidence in Reading and Writing of SHSTextual Evidence in Reading and Writing of SHS
Textual Evidence in Reading and Writing of SHSMae Pangan
 
Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Seán Kennedy
 
Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4JOYLYNSAMANIEGO
 
Keynote by Prof. Wurzer at Nordex about IP-design
Keynote by Prof. Wurzer at Nordex about IP-designKeynote by Prof. Wurzer at Nordex about IP-design
Keynote by Prof. Wurzer at Nordex about IP-designMIPLM
 
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...JojoEDelaCruz
 
Multi Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleMulti Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleCeline George
 
Using Grammatical Signals Suitable to Patterns of Idea Development
Using Grammatical Signals Suitable to Patterns of Idea DevelopmentUsing Grammatical Signals Suitable to Patterns of Idea Development
Using Grammatical Signals Suitable to Patterns of Idea Developmentchesterberbo7
 
ANG SEKTOR NG agrikultura.pptx QUARTER 4
ANG SEKTOR NG agrikultura.pptx QUARTER 4ANG SEKTOR NG agrikultura.pptx QUARTER 4
ANG SEKTOR NG agrikultura.pptx QUARTER 4MiaBumagat1
 
Congestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationCongestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationdeepaannamalai16
 
MECHANISMS OF DIFFERENT TYPES OF HYPERSENITIVITY REACTIONS.pptx
MECHANISMS OF DIFFERENT TYPES OF HYPERSENITIVITY REACTIONS.pptxMECHANISMS OF DIFFERENT TYPES OF HYPERSENITIVITY REACTIONS.pptx
MECHANISMS OF DIFFERENT TYPES OF HYPERSENITIVITY REACTIONS.pptxAnupkumar Sharma
 
Active Learning Strategies (in short ALS).pdf
Active Learning Strategies (in short ALS).pdfActive Learning Strategies (in short ALS).pdf
Active Learning Strategies (in short ALS).pdfPatidar M
 

Recently uploaded (20)

Transaction Management in Database Management System
Transaction Management in Database Management SystemTransaction Management in Database Management System
Transaction Management in Database Management System
 
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
 
The State of AI in Insights and Research 2024: Results and Findings
The State of AI in Insights and Research 2024: Results and FindingsThe State of AI in Insights and Research 2024: Results and Findings
The State of AI in Insights and Research 2024: Results and Findings
 
Oppenheimer Film Discussion for Philosophy and Film
Oppenheimer Film Discussion for Philosophy and FilmOppenheimer Film Discussion for Philosophy and Film
Oppenheimer Film Discussion for Philosophy and Film
 
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxMULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
 
Mattingly "AI & Prompt Design: Large Language Models"
Mattingly "AI & Prompt Design: Large Language Models"Mattingly "AI & Prompt Design: Large Language Models"
Mattingly "AI & Prompt Design: Large Language Models"
 
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONTHEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
 
Textual Evidence in Reading and Writing of SHS
Textual Evidence in Reading and Writing of SHSTextual Evidence in Reading and Writing of SHS
Textual Evidence in Reading and Writing of SHS
 
Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...
 
Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4Daily Lesson Plan in Mathematics Quarter 4
Daily Lesson Plan in Mathematics Quarter 4
 
Keynote by Prof. Wurzer at Nordex about IP-design
Keynote by Prof. Wurzer at Nordex about IP-designKeynote by Prof. Wurzer at Nordex about IP-design
Keynote by Prof. Wurzer at Nordex about IP-design
 
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptxYOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
 
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
ENG 5 Q4 WEEk 1 DAY 1 Restate sentences heard in one’s own words. Use appropr...
 
Multi Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP ModuleMulti Domain Alias In the Odoo 17 ERP Module
Multi Domain Alias In the Odoo 17 ERP Module
 
Using Grammatical Signals Suitable to Patterns of Idea Development
Using Grammatical Signals Suitable to Patterns of Idea DevelopmentUsing Grammatical Signals Suitable to Patterns of Idea Development
Using Grammatical Signals Suitable to Patterns of Idea Development
 
LEFT_ON_C'N_ PRELIMS_EL_DORADO_2024.pptx
LEFT_ON_C'N_ PRELIMS_EL_DORADO_2024.pptxLEFT_ON_C'N_ PRELIMS_EL_DORADO_2024.pptx
LEFT_ON_C'N_ PRELIMS_EL_DORADO_2024.pptx
 
ANG SEKTOR NG agrikultura.pptx QUARTER 4
ANG SEKTOR NG agrikultura.pptx QUARTER 4ANG SEKTOR NG agrikultura.pptx QUARTER 4
ANG SEKTOR NG agrikultura.pptx QUARTER 4
 
Congestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentationCongestive Cardiac Failure..presentation
Congestive Cardiac Failure..presentation
 
MECHANISMS OF DIFFERENT TYPES OF HYPERSENITIVITY REACTIONS.pptx
MECHANISMS OF DIFFERENT TYPES OF HYPERSENITIVITY REACTIONS.pptxMECHANISMS OF DIFFERENT TYPES OF HYPERSENITIVITY REACTIONS.pptx
MECHANISMS OF DIFFERENT TYPES OF HYPERSENITIVITY REACTIONS.pptx
 
Active Learning Strategies (in short ALS).pdf
Active Learning Strategies (in short ALS).pdfActive Learning Strategies (in short ALS).pdf
Active Learning Strategies (in short ALS).pdf
 

Nature_of_Roots_of_Quadratic_Equation.pptx

  • 1. YES-NO-STAND-UP Game Questions: 1. Do you like chocolates? 2. Do you like to hurt people? 3. Do you love math? 4. Is 2 + 2 = 5? 5. Is 9= 3 ? 6. Is 4 a perfect square? 7. Is 1 x 2 = 3? 8. Is 100 not a perfect square? 9. Is there a way to predict the nature of the root? 10. Are you familiar with discriminant in a quadratic? equation?
  • 2. NATURE OF ROOTS OF QUADRATIC EQUATION
  • 3. At the end of this lesson, the students are expected to: Objectives b. describes the nature of roots of a quadratic equation through its discriminant; c. value the importance of discriminant through the roots of the quadratic equation. a. identifies the nature of roots of a given quadratic equation;
  • 4. Group Activity 1. 𝒙𝟐 + 𝟒𝒙 + 𝟑 = 𝟎 2. 𝒙𝟐 − 𝟏 = 𝟎 Boys vs. Girls Direction: Find the roots of the quadratic eaquation using quadratic formula. Boys group will answer #1 and girls group will answer the #2. The groups have 5 minutes to answer and choose a representative to present their answer.
  • 5. Questions from the activity: 1. What is the standard form of the quadratic equation? 2. What is the formula for quadratic formula? 3. What is the formula of a discriminant? 4. Why do we need to determine the discriminant of the quadratic equation?
  • 6.
  • 7. WHY USE THE QUADRATIC FORMULA?  The quadratic formula allows you to solve ANY quadratic equation, even if you cannot factor it.  An important piece of the quadratic formula is what’s under the radical: b2 – 4ac  This piece is called the discriminant.
  • 8. WHY IS THE DISCRIMINANT IMPORTANT? The value of the expression 𝒃𝟐 – 4ac is called the discriminant of the quadratic equation ax² + bx + c = 0. This value can be used to describe the nature of the roots of a quadratic equation. It can be zero, positive and perfect square, positive but not perfect square or negative. ???
  • 9. Nature of Roots of Quadratic Equation Discriminant • It is the number being used to describe the nature of roots of a quadratic equation. Formula: d = b2 – 4ac provided that the equation is in standard form. discriminant Nature of Roots d = 0 real numbers and equal roots d > 0 d is a perfect square rational numbers and unequal roots d is not a perfect square irrational numbers and unequal roots d < 0 No real roots
  • 10. 9 Remember: Equation must be in standard form Example 1: Describe the nature of roots of 3t2 + 5t = 2 Solution: 3t2 + 5t = 2 Step 1: Write first the equation into standard form: 3t2 + 5t – 2 = 0 Step 2: Identify a, b and c a = 3, b = 5, c = –2 Step 3: Substitute these values to d = b2 – 4ac d = (5)2 – 4(3)(–2) d = 25 + 24 d = 49 Nature of Roots: rational numbers and equal discriminant Nature of Roots d = 0 real numbers and equal roots d > 0 d is a perfect square rational and unequal roots d is not a perfect square irrational and unequal roots d < 0 No real root
  • 11. Remember: Equation must be in standard form Example 2: Compute for the discriminant of (x – 2)2 = 0 Solution: Step 1: Write first the equation into standard form: x2 – 4x + 4 = 0 Step 2: Identify a, b and c a = 1, b = –4, c = 4 Step 3: Substitute these values to d = b2 – 4ac d = (–4)2 – 4(1)(4) d = 16 – 16 d = 0 Nature of Roots: real numbers and equal discriminant Nature of Roots d = 0 real numbers and equal d > 0 d is a perfect square rational numbers and unequal d is not a perfect square irrational numbers and unequal d < 0 No real roots
  • 12. Remember: Equation must be in standard form Example 3: What is the nature of roots of h2 – 16 = – 3h Solution: Step 1: Write first the equation into standard form: h2 + 3h – 16 = 0 Step 2: Identify a, b and c a = 1, b = 3, c = –16 Step 3: Substitute these values to d = b2 – 4ac d = (3)2 – 4(1)(–16) d = 9 + 64 d = 73 Nature of Roots: irrational numbers and unequal discriminant Nature of Roots d = 0 real numbers and equal d > 0 d is a perfect square rational numbers and unequal d is not a perfect square irrational numbers and unequal d < 0 No real roots
  • 13. Remember: Equation must be in standard form Example 4: Describe the nature of roots of the equation k2 - 3k = - 6 Solution: Step 1: Write first the equation into standard form: k2 - 3k + 6 = 0 Step 2: Identify a, b and c a = 1, b = -3, c = 6 Step 3: Substitute these values to d = b2 – 4ac d = (-3)2 – 4(1)(6) d = 9 – 24 d = – 15 Nature of Roots: No real roots discriminant Nature of Roots d > 0 d is a perfect square • Two real, rational and unequal roots d is not a perfect square • Two real, irrational and unequal roots d = 0 • One real and rational root. d < 0 • No real root discriminant Nature of Roots d = 0 real numbers and equal d > 0 d is a perfect square rational numbers and unequal roots d is not a perfect square irrational numbers and unequal roots d < 0 No real root
  • 14. Remember: Equation must be in standard form Example 5: Determine the nature of roots of the equation 3x2 + 11x + 8 = 0 Solution: Step 1: Write first the equation into standard form: 3x2 + 11x + 8 = 0 Step 2: Identify a, b and c a = 3, b = 11, c = 8 Step 3: Substitute these values to d = b2 – 4ac d = (11)2 – 4(3)(8) d = 121 – 96 d = 25 Nature of Roots: rational numbers and unequal discriminant Nature of Roots d = 0 real numbers and equal d > 0 d is a perfect square rational numbers and unequal roots d is not a perfect square irrational and unequal roots d < 0 No real root
  • 15. Activity Place Me on the Table! Direction: Answer the following. 1. Complete the table below. Equation b²-4ac Nature of roots 1. x² + 5x + 4 = 0 2. 2x² + x - 21= 0 3. 4x² +4x + 1 = 0 4. x² - 2x - 2 = 0 5. 9x² + 16= 0 2. How would you describe the roots of quadratic equation when the value of b²- 4ac is 0? Positive and Perfect Square? Positive but not Perfect Square? Negative? . 3. Which quadratic equation has roots that are real numbers and equal? Rational numbers? Irrational numbers? Not real numbers? 4. How do you determine the quadratic equation having roots that are real numbers and equal? Rational numbers? Irrational numbers? Not real numbers?
  • 16. Directions: Determine the discriminants and nature of the roots of the following quadratic equations. Write your answer on the space provided. Evaluation 2. 𝑥2 + 9𝑥 + 20 = 0 1. 𝑥2 + 6𝑥 + 9 = 0 3. 2𝑥2 − 10𝑥 + 8 = 0 4. 𝑥2 + 5𝑥 + 10 = 0 5. 𝑥2 + 6𝑥 + 3 = 0 discriminant: discriminant: discriminant: discriminant: discriminant: nature of the roots nature of the roots nature of the roots nature of the roots nature of the roots
  • 17. Assignment: Study Sum and Product of Roots of a Quadratic Equation.