This document provides a daily lesson log for a Grade 9 mathematics class. It outlines the objectives, content, learning resources and procedures for lessons on the nature of roots of quadratic equations, including the sum and product of roots, and equations that can be transformed into quadratic equations. Key concepts covered are using the discriminant to characterize roots, the relationship between coefficients and roots, and solving various types of equations. Examples and follow-up questions are provided to discuss and practice the new skills.

1. GRADES 9
DAILY LESSON LOG
School Grade Level 9
Teacher Learning Area MATHEMATICS
Teaching Dates and
Time
Quarter FIRST
Teaching Day and Time
Grade Level Section
Session 1 Session 2 Session 3 Session 4
I. OBJECTIVES
1. Content StandardsThe learner demonstrates understanding of key concepts of quadratic equations, inequalities and functions, and
rational algebraic equations.
2. Performance
Standards
The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real-life
problems involving quadratic equations, inequalities and functions, and rational algebraic equations and solve them
using a variety of strategies.
3. Learning
Competencies/
Objectives
Characterizes the roots of a
quadratic equation using
the discriminant.
(M9AL-Ic-1)
a. Evaluate the expression
given the b2 – 4ac values of
a, b, and c
b. Use the discriminant in
characterizing the roots of
quadratic equations
c. Appreciate the
importance of discriminant
Describes the relationship
between the coefficients and
the roots of a quadratic
equation. (M9AL-Ic-2)
a. Describe the relationship
between the coefficients and
the roots of quadratic
b. Determine the sum of the
roots of quadratic equations
c. Value the knowledge as a
means of new understanding
Describes the relationship
between the coefficients and
the roots of a quadratic
equation. (M9AL-Ic-2)
a. Describe the relationship
between the coefficients and
the roots of quadratic
b. Determine the product of
the roots of quadratic
equations
c. Appreciate the importance
of quadratic equation in real-
life situation
Solves equations
transformable to quadratic
equations (including rational
algebraic equation).
(M9AL-Ic-d-1)
a. Transform quadratic
equation into standard form
b. Find the solutions of
equations transformable to
quadratic equations
c. Show self-reliance and
display interests when
working independently
II. CONTENT Nature of Roots of
Quadratic Equation
Sum of the Roots of
Quadratic Equations
Product of the Roots of
Quadratic Equations
Equations Transformable to
Quadratic Equations

2. III. LEARNING
RESOURCES
A. References
1. Teacher’s
Guide pp. 39-44 pp. 45-49 pp. 45-49 pp. 50-53
2. Learner’s
Materials pp. 56-63 pp. 66-72 pp. 66-72 pp. 77-87
3. Textbook
Our World of Math
pp. 21-25
21st Century Mathematics
pp. 168-172
Ju Se T. Ho et.al
21st Century Mathematics
pp. 168-172
Ju Se T. Ho et.al
Intermediate Algebra
pp. 58-60
Julieta G. Bernabe et.al.
4. Additional
Materials from
Learning
Resource (LR)
portal
http://www.purplemath.com
/moduleiquadraticform.htm
http://www.algebrahelp.co
m/lessons/equation/quadrat
ic
http://www.athometuition.com/
QuadraticEquationFormula.ph
http://www.math-help-
ace.com/Quadratic-Equation-
Solver.html
http://www.athometuition.co
m/QuadraticEquationFormul
a.ph
http://www.math-help-
ace.com/Quadratic-
Equation-Solver.html
B. Other Learning
Resources
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
activity sheets, laptop and
monitor
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
activity sheets, laptop and
monitor
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
activity sheets, laptop and
monitor
Grade 9 LCTG by DepEd
Cavite Mathematics 2016,
activity sheets, laptop and
monitor
IV. PROCEDURES
A.Reviewing previous
lesson or presenting
the new lesson
Preliminary Activity:
1. Evaluate the expression
b2 – 4ac given the following
values of a, b, and c.
1. a =1 , b = 5, c = 4
2. a = 2, b = 1, c = -21
3. a = 4, b = 4, c = 1
4. a = 1, b = -2, c = -2
Let’s Do Addition!
Perform the indicated
operation.
1. 7+15 =
2. -9 + 14 =
3. -6 + (-17) =
Determine the roots of each
quadratic equation using any
method.
1. x2 + 7x + 12 = 0
= ____ , = ____
2. 2x2 – 3x – 20 = 0
= ____ , = ____
Preliminary Activity:
Showing different equations
on the TV screen and letting
each learner study the given
equation.
1.
2. (x+1) (x – 2) = 12

3. 5. a = 9, b = 0, c = 16
4. + =
5. + =
Quadrati
c
Equation
Sum
of
Roots
Product
of
Roots
x2 + 7x +
12 =0
2x2 – 3x
– 20 = 0
3. x(x – 3) = 20
4.
5.
B.Establishing a
purpose for the
lesson
1. Where you able to find
the expression b2 - 4ac
given the values of a, b,
and c?
2. What do you think is the
importance of the
expression b2 – 4ac in
determining the nature of
the roots of a quadratic
equation?
1. How did you determine the
result of each operation?
2. What mathematics
concepts and principles did
you apply to arrive at each
result?
3. Compare your answers
with those of your classmates.
Did you arrive at the same
answers? If NOT, explain
why.
1. What do you observe
about the sum and product
of the roots of each
quadratic equation in
relation to the values a, b, c?
2. Do you think a quadratic
equation can be determined
given its roots or solutions?
Justify your answer by giving
3 examples
1. Which of the given
equations are written in
Standard Form?
2. How do you describe
standard form of equation?
C.Presenting examples/
instances of the
lesson
Examples:
1. x2 – 2x + 1 = 0
D = b2 – 4ac
D = (-2)2 – 4(1)(1)
D = 4 – 4
The sum of the roots of the
quadratic equation ax2 + bx +
c = 0 can be determined using
the coefficients a, b, and c.
Remember that the roots of
a quadratic equation can be
determined using the formula
The product of the roots of
the quadratic equation
+ bx + c = 0 can be
determined using the
coefficients a, b, and c.
Remember that the roots
of a quadratic equation can
be determined using the
formula
Solving Quadratic Equations
That are Not Written in
Standard Form
Example 1: Solve x(x – 5) =
36

4. D = 0
Therefore the roots are
real, rational, and equal.
2. 3x2 – x – 2 = 0
D = b2 – 4ac
D = (- 1)2 – 4(3)(-2)
D = 1 + 24 D = 25
Since D ˃ 0 and a perfect
square
Therefore the roots are
real, rational, and unequal.
3. x2 – 6x + 7 = 0
D = b2 – 4ac D = (-6)2 –
4(1)(7)
D = 36 – 28
D = 8 Since
D ˃ 0 and not a perfect
square.
Therefore the roots are
real, irrational and unequal.
4. x2 – 4x + 5 = 0
From the quadratic formula,
let and
be the
roots.
Example 1. Find the sum of
the roots of + 8x – 10 = 0
Sum of the roots =
The sum of the roots of
+ 8x – 10 = 0 is - 4
Example 2. Use the values of
a, b and c in finding the roots
of the quadratic equation.
The values of a, b, and c in
the equation are 1, 7 and -18,
respectively. Use this value to
find the sum and the product
of the roots of the equation.
Sum of the roots =
The sum of the roots of +
From the quadratic formula,
let
and
be the
roots.
Example 1. Find the sum of
the roots of + 8x – 10 =
0
Product of the roots =
The product of the roots of
+ 8x – 10 = 0 is -5
Example 2. Use the values
of a, b and c in finding the
roots of the quadratic
equation.
The values of a, b, and c in
the equation are 1, 7 and -
18, respectively. Use this
value to find the sum and
Example 2: Find the roots of
the equation
(2x - 2)(x + 4) = 0
2x – 2 = 0 or x + 4 = 0
X = 1 or x = -4

5. D = b2 – 4ac
D = (-4)2 – 4(1(5)
D = 16 – 20
D = - 4
Since D ˂ 0 therefore the
roots are not real or
imaginary.
7x – 18 = 0 is -7 the product of the roots of
the equation.
Product of the roots =
The product of the roots of
+ 7x – 18 = 0 is -18
D.Discussing new
concepts and
practicing new skills
#1
Using the values of a, b,
and c, write the quadratic
equation ax2+bx+c= 0.
Then find the roots of each
resulting equation.
1. a =1 ,b = 5, c = 4
2. a = 2,b = 1,c =-21
3. a = 4,b = 4, c = 1
4. a = 1,b = -2,c = -2
5. a = 9, b = 0, c = 16
Direction: Determine the sum
of the roots by using .
- 2x – 3 = 0
= 10x – 25
+ 2x – 5 = 0
+ 8x + 3 = 0
– 2x – 7 = 0
Direction: Determine the
product of the roots by using
c/a
- 2x – 6 = 0
= 10x – 36
+ 2x – 5 = 0
+ 8x + 6 = 0
– 2x – 14 = 0.
View Me in Another Way!
Transform each of the
following equations into a
quadratic equation in the
form .
1. x (x + 5)= 2
2.
3.
4.
5.

6. E.Discussing new
concepts and
practicing new skills
#2
Follow-up Questions:
1. Can we determine the
nature of the roots of a
quadratic equation without
solving the equation?
2. Can we identify whether
the roots are real, rational,
or irrational, equal or
unequal?
3. When will the equation
have no real roots?
Follow-up Questions:
1. What is the relation
between the coefficients and
the roots of quadratic
equation?
2. How can the sum of the
roots be obtained?
3. How do you check your
answer?
Follow-up Questions:
1. What is the relation
between the coefficients and
the roots of quadratic
equation?
2. How can the product of
the roots be obtained?
Follow-up Questions:
1. How did you transform
each equation into a
quadratic equation?
2. What mathematics
concepts or principles
did you apply?
3. Did you find any
difficulty in
transforming each
equation into a
quadratic equation?
Explain.
F. Developing mastery
(Leads to Formative
Assessment 3)
Solve for the discriminant
of the following quadratic
equation and determine the
nature of the roots.
1. + 5p – 3 = 0
2. + 9r + 14 = 0
3. + 5x + 10 = 0
4. – 7x = 30
5. + 6x + 9 = 0
Direction: Find the sum of the
roots.
+ 4x + 3 = 0
+ 12x – 18 = 0
– 6x = 8
– 3x = 0
= 25
Direction: Find the product
of the roots.
+ 4x + 9 = 0
+ 12x – 36 = 0
– 6x = 18
– 16x = 0
= 36
Solve and Find the roots of
the following equations.
1.
2. (x – 10)(x + 3) = 0
3. x(x + 12) = 10
4.

7. 5. (x – 4)(x + 5) = 0
G.Finding practical
applications of
concepts and skills in
daily living
Directions: Study the
situation below and answer
the questions that follow.
Lola Nidora asks
Rogelio to make a table
which has an area of 6m2.
The length of the table has
to be 1 m longer the width.
1. If the width of the table
is p meters, what will be its
length?
2. Form a quadratic
equation that represents
the situation.
3. Without actually
computing for the roots,
determine whether the
dimensions of the table are
rational numbers. Explain.
4. Give the dimensions
of the table.
Answer the following problem.
1. Suppose the sum of the
roots of a quadratic equation
is given, do you think you can
determine the equation?
Justify your answer.
2. The sum of the roots of a
quadratic equation is -5. If one
of the roots is 7, how would
you determine the equation?
Write the equation.
Read and understand the
situation below to answer
the questions that follow.
1. Lola Nidora is informed
that his bodyguard Rogelio
owns a rectangular lot. The
perimeter of the lot is 90m
and its area is 450 m2.
a. What equation
represents the
perimeter of the lot?
b. How about the
equation that
represents the area?
c. How is the given
situation related to
the sum
and the product of the
roots of quadratic
equation?
d. What quadratic
equation can be
formed that
describes the
problem?
e. What are the
dimensions of the
rectangular lot?
My understanding of
Equations Transformable
into Quadratic!
Answer the following.
1. In a water refilling
station, the time that a
pipe takes to fill a tank
is 10 minutes more
than the time that
another pipe takes to
fill the same tank. If
the two pipes are
opened at the same
time, they can fill a
tank in 12 minute.
How many minutes
does each pipe take
to fill the tank?
2. A flare is launched
from a life raft with an
initial velocity of 80
meters per second.
How many seconds
will it take for the flare
to return to the sea?

8. 2. The perimeter of a
rectangular bulletin board is
20ft. if the area of the board
is 21ft. What are its length
and width?
H.Making
generalizations and
abstractions about
the lesson
If b2 –4ac = 0, the roots
are real, rational and equal.
If b2 –4ac ˃ 0 and a perfect
square, then the roots are
real, rational and unequal.
If b2 –4ac ˃ 0 and not a
perfect square, the roots
are unequal and irrational.
If b2 –4ac ˂ 0 the roots are
not real or imaginary.
Sum of the Roots of Quadratic
Equation
+
The sum of the roots of
quadratic equation is .
Product of the Roots of
Quadratic Equation
)
The sum of the roots of
quadratic equation is .
There are equations that are
transformable to quadratic
equations. These equations
may be given in different
forms. Hence, the
procedures in transforming
these equations to quadratic
equations may also be
different. Once the equations
are transformed to quadratic
equations, then they can be
solved using the different
methods of solving quadratic
equations, such as extracting
square roots, factoring,
completing the square and
using the quadratic formula.
An extraneous root of an
equation can be derived from
an original equation.
However, it is not a solution
of the original equation.
I. Evaluating learning “Where do you like to go in
Cavite?”
Direction: Characterize the
nature of the roots of the
following quadratic
Using the values of a, b, and
c, find the sum of the following
equations.
– 4x – 21 = 0
Using the values of a, b, and
c, find the product of the
following equations.
– 4x – 12 = 0
Let’s Be True!
Find the solution set of the
following.
1. x(x+3)=28

9. equations using the
discriminant. Use the
legend below.
Taal Volcano Water Camp
Kaybiang Tunnel Aguinaldo
Shrine
(real,rational,equal)
(real,rational,unequal)
(real,irrational, unequal)
(not real, imaginary)
1. + 9x + 20 =0
2. + 6x + 13 = 0
3. – 5x = - 4
4. – 2x – 5 = 0
5. + 8x + 16 = 0
– 8x = 48
= 1
– x + 6 = 0
-8x + 1 = 0
– 8x = 24
= -6
– x + 12 = 0
-8x + 3 = 0
2. 3s(s-2) = 12s
4. =65
J. Additional activities
for application or
remediation
Assignment:
Follow-up
Find the value of k
in each quadratic equation
in order to have:
Equal roots
a. + 2x + 1 = 0
b. + 4x + k = 0
2. Study the sum and
product of the roots of the
Assignment:
Study
1. Product of Roots of
Quadratic Equations
Assignment:
Determine the sum and the
product of each equation.
1. = 3c
2. (x – 2 =9
3. – 9b = 0
4. ( n – 7 = 6
5. 3(a + 7 + 4 = 49
Assignment:
Study the steps in
transforming rational
algebraic expressions into
quadratic equation.

10. quadratic equation.
a. How do you get the
sum and product of
quadratic equation?
b. Give the formula
V. REMARKS
VI. REFLECTION
a. No. of learners who
earned 80% on the
formative assessment
b. No. of learners who
require additional
activities for
remediation.
c. Did the remedial
lessons work? No. of
learners who have
caught up with the
lesson.
d. No. of learners who
continue to require
remediation
e. Which of my teaching
strategies worked
well? Why did these
work?

11. f. What difficulties did I
encounter which my
principal or supervisor
can help me solve?
g. What innovation or
localized materials did
I use/discover which I
wish to share with
other teachers?