SOLVING QUADRATIC EQUATIONS BY FACTORING

Solve the quadratic equations.

Problem 1 :

x² + 11x + 28 = 0

a. x = -7and -4                    c. x = -4 and 7

b. x = -7 and 4                    d. x = 4 and 7

Solution :

x² + 11x + 28 = 0

Leading coefficient = 1. 

x² + 4x + 7x + 28 = 0

x(x + 4) + 7(x + 4) = 0

(x + 7) (x + 4) = 0

So, option (a) is correct.

Problem 2 :

Factories the quadratic polynomial

6x² - 4x + 8

a. 6x(3x – 2)          c. 6x² – 4x + 8

b. 3(2x² – 4x + 8)         d. 2(3x² – 2x + 4)

Solution :

6x² - 4x + 8

= 2(3x² – 2x + 4)

So, option (d) is correct.

Problem 3 :

-12x² - 8x = 0

a. x = 0 and x = 12          c. x = 0 and x = -2

b. x = 0 and x = -2/3          d. x = 0 and x = -3/2

Solution :

-12x² - 8x = 0

-4x(3x + 2) = 0

-4x = 0 and 3x + 2 = 0

x = 0 and x = -2/3

So, option (b) is correct.

Problem 4 :

Solve by factoring.

4x² + 10x – 24 = 0

a.  3/2, -1         c. 4, -1

b. -4, 3/2          d. -4, 4

Solution :

4x² + 10x – 24 = 0

2(2x² + 5x – 12) = 0

Dividing 2 on both sides.

2x² + 5x – 12 = 0

By using algebraic expression

2x² + 8x – 3x – 12 = 0

2x(x + 4) – 3(x + 4) = 0

(2x – 3) (x + 4) = 0

2x – 3 = 0 and x + 4 = 0

2x = 3

x = 3/2 , x = -4

So, option (b) is correct.

Problem 5 :

6x² = 42

a. -√7, √42            c. √7, -√7

b. -√42/6, √42/6           d. √7

Solution :

6x² = 42

x² = 42/6

x² = 7

x = ±√7

So, option (c) is correct.