example

1. Republic ofthePhilippines
DepartmentofEducation
REGION VII - CENTRAL VISAYAS
DIVISION OF BAIS CITY
LONOY NATIONAL HIGH SCHOOL
ACTIVITY SHEET IN MATHEMATICS 9
Quarter First
Week No Two
Learning
Objectives
*Determineanddescribethenatureof the roots of the quadratic equationsusingthe
discriminant.
*Solve the discriminantofa quadratic equation.
*Developself- reliance
Topic/ Key
Concepts
Content
The roots of any quadratic equation can be found by using any of the four methods (a) extracting
squareroots (b) factoring (c) completing the square (d) quadratic formula. Note that a quadratic equation
mayhave onerealnumbersolution,two realnumbersolution,orno real numbersolution.Thenumberand
kindof solutionof quadratic equationscanbedeterminedfrom apart of the quadratic formula, that is, from
𝑏² – 4𝑎𝑐.
This portion of the quadratic formula that determines the nature of roots of a quadratic equation is
called the discriminant.
DISCRIMINANT OF A QUADRATIC EQUATION
 Theexpression 𝑏2 − 4𝑎𝑐 in the quadratic formulaiscalledthediscriminant.
 Thediscriminantgivesimportantinformationaboutthecorrespondingsolutionsorroots
𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0of wherea, b, and c are realnumbersand 𝑎 ≠ 0 .
 Therootsof anyquadratic equation,𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0, are the pointson the x – axis where the graph
crosses.
Nature and Number of Roots of a Quadratic Equation
Discriminant Nature of Roots
Number of
Solution
Graph
𝑏² – 4𝑎𝑐 = 0 Real and Equal One solution
𝑏² – 4𝑎𝑐 > 0
perfect square
Rational and
Unequal Two distinct
solutions
not perfect
square
Irrational and
Unequal
b² – 4ac < 0 Imaginary No Solution
Procedures EXAMPLE1: Determinethenatureof the roots of eachequation.
A. x2 – 6x + 9 = 0 C. 2x2 – 4x + 5 = 0
B. x2 + 6x + 5 = 0 D. 5x2 – x – 2 =0
SOLUTION:
A. x2 – 6x + 9 = 0 a = 1, b = 6, andc = 9
D = b2 – 4ac
D = 62 – 4(1)(9) Since D= 0, the roots of x2 – 6x + 9 = 0 are real, equal,andrational.
D = 36 – 36
D = 0
B. x2 + 6x + 5 = 0 a = 1, b = 6, andc = 5
D = b2 – 4ac
D = 62 – 4(1)(5) Since D = 16, whichisa perfect square,the roots of x2 + 6x + 5 = 0 are
D = 36 – 20 real,unequal,andrational.

2. D = 16
C. 2x2 – 4x + 5 = 0 a = 2, b = -4, andc = 5
D = b2 – 4ac
D = (-4)2 – (4)(2)(5) Since D = -24, the roots of 2x2 – 4x + 5 = 0 are imaginary andunequal.
D = 16 – 40
D = -24
D. 5x2 – x – 2 =0 a = 5, b = -1, and c = -2
D = b2 – 4ac
D = (-1)2 – 4(5)(-2) Since D = 41, the roots of 5x2 – x – 2 =0 arereal, unequal,and
D = 1 + 40 irrational.
D = 41
Activity 1: Math in A, B, C?
Directions:Write the followingquadratic equationsinstandardform,
ax² + bx + c = 0, then identifythe values of a, b, andc. Answer the questionbelow.
Write your answerona sheet of paper.
ax² + bx + c = 0
1. x² + 5x = 4 _______________a= ____b = ____c = _____
2. -4x2 = 8x – 3 _______________a=____b = ____c = _____
3. 10x – 1 = 4x² _______________a=____b = ____c = _____
4. 15 + 8x – 3x2 = 0 _______________a= ____b = ____c = _____
5. 3x(x – 14)= 12 _______________a= ____b = ____ c = _____
Questions: How did you write quadratic equation in standard form?
Activity 2: Find My Equations and Roots
Directions: Evaluate the expressionb²– 4ac given the followingvalues of a, b, andc then
completethetablebelow.Write your answeron a sheet of paper.
1. a = 1, b = 5, c = 4 4. a = 1, b = - 2, c = -2
2. a = 2, b = 1, c = -21 5. a = 9, b = 0, c = 16
3. a = 4, b = 4, c = 1
Equation b² - 4ac Roots
1.
2.
3.
4.
5.
Activity 3: What is My Nature?
Directions:Determinethenature of the roots of the followingquadratic equationsusingthe
discriminant.Answerthe questionsthat follow.
1. x2 + 6x + 9 = 0 discriminant:______natureof the roots: _________
2. x2 + 9x + 20 = 0 discriminant: ______natureof the roots: _________
3. 2x2 – 10x+ 8 = 0 discriminant: ______ natureof the roots: _________
4. x2 + 5x + 10 = 0 discriminant: ______ natureof the roots: _________
5. x2 + 6x + 3 = 0 discriminant: ______ nature of the roots: _________
6. 2x2 + 6x + 4 = 0 discriminant: ______ nature of the roots: _________

3. Prepared by:
BOBBY B. ONG
Teacher 1
Reminder:
*makeyour ACTIVITY 1 (or even up to 3) as practiceofthe lesson introduced
*your ACTIVITY 2 (or even 4- 5) as abstractionandsynthesis of the lesson
7. 3x2 – 5x = -4 discriminant: ______ natureof the roots: _________
8. 9x2 – 6x = -9 discriminant: ______natureof the roots: _________
9. 10x2 – 4x = 8 discriminant:______natureofthe roots: _________
10. 3x² – 2x – 5 = 0 discriminant:______natureof the roots: _________
Assessment
Pleaseanswerthe WeeklyHomeLearning Plan (theteachermayopt to provide additionalactivities
dependingonthecapabilityof the learnerinvolve)
References Learner’sModule,Lesson 3,page65-76