Page 6 - CHAPTER 4 (Quadratic equations)

CHAPTER 4

QUADRATIC EQUATIONS

Step 2: Express the coefficient of the middle term (coefficient of x) as
the sum or difference of the factors obtained in step 1. The product of

the set wo factors will be equal to the product of the coefficient of x 2

and the constant term.

Step 3: Split the middle term in two parts obtained in step 2.

Step 4: Factorize the quadratic equation obtained in step 3 by
grouping the terms method.

Try and learn

Example 4: Solve the below quadratic equation by factorization

method x²-2ax+a²-b²=0.

Solution: Factors of the constant term a²-b² are (a – b) & (a + b) also

coefficient of the middle term = –2a = – [(a – b) + (a + b)]

⇒ x²-2ax+a²-b²=0

⇒x²-{(a-b)+ (a+b)}x+(a+b)(a-b)=0

⇒x²-(a-b)x-(a+b)x+(a-b)(a+b)= 0

⇒x [x-(a-b)]- (a+b)[x-(a-b)]= 0

⇒[x-(a-b)][x-(a+b)]= 0

x-(a-b)=or x-(a+b)= 0, x=a-b, x=a+b

Example 5: Solve the quadratic equation 5x²= -16x-12 by factorization

method.

2
Solution: 5x = -16x-12
2
5x +16x+12=0
2
5x +10x+6x+12=0

5x(x+2)+ 6 (x+2)= 0

(x+2)(5x+6)= 0

x+2=0 ⇒x= -2

-6
5x+6=0 ⇒x=
5

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