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UNLOCK THE POWER OF
QUADRATIC EQUATIONS
BY JOHN EKPENYONG

OBJECTIVES
 At the end of this lesson student should be able to :
 - define quadratic equation
 Identify the three methods used in solving quadratic equation
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QUADRATIC EQUATION

Definition of Quadratic Equation

A quadratic is an equation in which the highest
power of an unknown quantity is a square
...
They are :
- Factoring
- The quadratic formula (almighty formula)

- Completing the square

Factoring method
To solve a quadratic equation by factoring :
1
...

2
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Set each factor equal zero
4
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Check by inserting your answer in the original equation
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Solution
Set the right side to zero
Factor the left side (2x-3)(x+4)=0
Set each factor to zero : 2x-3=0 or x+4=0
Solve each equation : x =3/2 or x =-4
The solution set is { 3/2, -4 }

 3
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Solution
X2-3x-10=0
Factor the left side : (x-5)(x+2)=0
Set each factor to zero :
x-5=0 or x+2
solve each equation : x=5 or x=-2
The solution set is { 5, -2 }

The quadratic formula (almighty formula)
 Examples
1) Solve x2 +5x-14=0 sing the quadratic or the almighty formula
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244

or

v= 0
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Solve the equation 2x 2 + 9x-5
(a) x=1/2 , 5= -5 (b) x = -2 ,x=3 (c) x =0
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Solve the equation 2s 2 + 5s=3
(a)
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Solve x2-3x-10=0
(a)
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{ 9,-5 }

4
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X= 4
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30

(b) x= -3
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2 (c) x=-12, or -13 (d)x= -11, or 5
(next page)

5
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A
 2
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A
 4
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D

Theory practice questions
Solve x2 - 6x +5 =0 using the almighty formula
Solution
X2 – 6x +5 =0
Compare with ax2 + bx +c =0
Where a = 1, b=-6 and c =5
X = -b ± √b2 -4ac
2a
X= 6 ± √ 62-4(1)(5)
2(1)

(next page )

X= 6 ± √ 36-20
2
X= 6 ± √ 16
2
X= 6 ± 4
2
X= 6 + 4

or

6-4

2

2

X= 10/2
X=5

2/2
or

1

(final answer)

2

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