Lesson Plan in Mathematics 9
I.OBJECTIVES
A. Content Standard
The learner demonstrates understanding of key concepts of quadratic equation.
B. Performance Standard
The learner is able to investigate thoroughly mathematical relationships in various situations,
formulate real – life problems involving quadratic equation.
C. Learning Competency
The learner characterizes the roots of a quadratic equation using discriminant. M9AL–Ic-1
In this lesson, the students should be able to:
Describe the nature of the roots of a quadratic equation using the value of the
discriminant.
Solve the Discriminant of a quadratic equation.
Appreciate the importance of the discriminant to real life setting.
II. CONTENT and MATERIALS
The Nature of the Roots of a Quadratic Equations
Teacher’s Guide (TG) in Mathematics 9, pp. 39-44
Content:
References:
Learner’s Module (LM) in Math 9, pp. 56-65
laptop, TV, PowerPoint, worksheets, Manila paper, pentel pen, chalk
Materials:
III. Procedure
A. ACTIVITY
Activity 1 Stand-Up or Sit Down
Directions: Given the situations below, identify if the statement is REAL or Not REAL. If
the situation is REAL means “Stand-up”, if the situation is Not REAL means “Sit down”.
The LGBT community is given
the same rights with men and
women of today’s generation.
Men are more powerful than
women.
Discrimination is always done
on purpose.
Activity 2 Am I Real or Not Real
Discrimination can only happen
in the workplace.
Discrimination and bullying of people
remain a threat to people’s freedom
and welfare.
Directions: Put a check (✓) on the corresponding box that best describes the given
numbers. Answer the questions that follow.
Not Real Numbers
Real Numbers
1. 0
2. 1/2
3. √64
4. √-9
5. 169
Activity 3 Do I know my ABC?
Directions: Tell whether the given quadratic equations are in standard form or
not. If not, rewrite the equation in the form ax2 + bx + c = 0, then identify the
values of a, b, and c.
1) 6x² – 2x = 3
________________
a= ____ b= ____ c= ____
2) 3x² – 5 = 2x
________________
a= ____ b= ____ c= ____
3) x² – 12x = -36
________________
a= ____ b= ____ c= ____
4) 3x² + 2 = -4x
________________
a= ____ b= ____ c= ____
5) x² + 6x = -2
________________
a= ____ b= ____ c= ____
B. ANALYSIS






Which of the following numbers above are familiar to you? Why? Describe these
numbers.
Which of the numbers are rational? Irrational? Explain your answer.
Which of the numbers are perfect squares? Not perfect squares?
How do you describe numbers that are perfect squares?
Where you able to write the equations in standard form? How?
Is there another way of writing each quadratic equation in standard form? If yes,
show and determine the values of a, b and c.
Activity 4: Find the Value of b2 - 4ac
Directions: Evaluate the expression b2 - 4ac given the following values of a, b, c.
1. 𝑎 = 6
𝑏 = −2
𝑐 = −3
2. 𝑎 = 3
𝑏 = −2
𝑐 = −5
3. 𝑎 = 1
𝑏 = −12
𝑐 = 36
4. 𝑎 = 3
𝑏=4
𝑐=2
5. 𝑎 = 1
𝑏=6
𝑐=2
C. ABSTRACTION
What is a quadratic equation?
What should first to consider before finding a, b, and c?
How can we find the roots or solutions of a quadratic equation?
How many roots or solutions can a quadratic equation have?
We have already studied the quadratic formula,
-b ± √b2 – 4ac
x=
2a
The binomial inside the radical sign is called the discriminant. It is used to determine the
nature of the roots of a quadratic equation. We can also determine the number of real roots
for a quadratic equation with this number. The following table will give us the relation
between the discriminant and the nature of the roots.
The value of the expression b2 - 4ac is called the discriminant of the quadratic equation,
denoted by D = b2 – 4ac. This value can be used to describe the nature of the roots of a
quadratic equation. It can be zero, positive perfect square, positive but not a perfect square,
or negative.




Discriminant
Nature of the Roots
Number of real roots
b2 – 4ac = 0
Real and Equal
1
b2 – 4ac > 0 and a perfect square
Rational and Unequal
2
b2 – 4ac > 0 but not a perfect square
Irrational and Unequal
2
b2- 4ac < 0
Imaginary/No Real
Roots
None
D. APPLICATION
The class will be divided into 5 groups. Then, each group will be given different set of
worksheets. After 10 minutes, each output will be presented to the class.
Group 1.
Nature of the Roots
Equation
a
b
c
Discriminant
𝑥 2 − 4𝑥 + 4 = 0
𝑥 2 + 9𝑥 + 20 = 0
Group 2.
Equation
a
b
c
Discriminant
Nature of the Roots
a
b
c
Discriminant
Nature of the Roots
a
b
c
Discriminant
Nature of the Roots
a
b
c
Discriminant
Nature of the Roots
𝑥 2 + 7𝑥 + 10 = 0
2𝑥 2 + 5𝑥 + 4 = 0
Group 3.
Equation
𝑥 2 + 6𝑥 + 3 = 0
𝑥 2 − 10𝑥 + 25 = 0
Group 4.
Equation
𝑥 2 + 2𝑥 + 5 = 0
2𝑥 2 + 6𝑥 + 4 = 0
Group 5.
Equation
𝑥 2 + 6𝑥 + 9 = 0
𝑥 2 + 2𝑥 + 3 = 0
Criteria
10
8
5
0
Presentation
Explains
mathematical
procedures
without difficulty
and provides
full explanations
for how answers
are derived.
Explains
mathematical
procedures
without difficulty
and provides
partial
explanations for
how answers
are derived.
Explains
mathematical
procedures
but
encounters
difficulty on it.
NO
PRESENTATION
IV. Evaluation
Directions: Read each item carefully. Choose only the letter of the correct answer.
1. How many roots are there if the discriminant of a quadratic equation is greater than zero?
A. 1 real root
C. 3 real roots
B. 2 real roots
D. No Solutions
2. What is the nature of the roots of the quadratic equation if the value of its discriminant is
zero?
A. The roots are not real
C. The roots are rational and not equal.
B. The roots are irrational and not equal. D. The roots are rational and equal.
3. What is the nature of the roots of the quadratic equation if the value of its discriminant is
greater than zero but a perfect square?
A. The roots are not real
C. The roots are rational and not equal.
B. The roots are irrational and not equal. D. The roots are rational and equal.
4. The coefficients of a quadratic equation are all integers. The discriminant is 0 but not a
perfect square. Which statement best describes its roots?
A. Two irrational roots
C. One rational root
B. No Real Roots
D. Two rational roots
5. How many real roots does the quadratic equation x2 + 5x + 7 = 0 have?
A. 0
B. 1
C. 2
D. 3
V. Assignment
Read and Study about the Sum and Product of Roots of Quadratic Equations and answer
the following.
1. What is the formula in finding the sum of the roots?
2. What is the formula in finding the product of the roots?
Prepared by:
ERICSON T. CABRERA
Teacher I
Observer:
RODOLFO O. DELA CRUZ JR.
Master Teacher I
ETHEL M. RECILLA
Master Teacher II