Question

What are the solutions of the quadratic equation

4x2 - 8x – 12 = 0 ?
A) x = -1 and x = -3
B) x = -1 and x = 3
C) x = 1 and x = -3
D) x = 1 and x = 3

Answer 1

B IS THE ANSWER

Step-by-step explanat

(22x2 - 8x) - 12 = 0

4x2 - 8x - 12 = 4 • (x2 - 2x - 3)

The first term is, x2 its coefficient is 1 .

The middle term is, -2x its coefficient is -2 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3

Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is -2 .

-3 + 1 = -2 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 1

x2 - 3x + 1x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-3)

Add up the last 2 terms, pulling out common factors :

1 • (x-3)

Step-5 : Add up the four terms of step 4 :

(x+1) • (x-3)

Which is the desired factorization

4 • (x + 1) • (x - 3) = 0

A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

Any solution of term = 0 solves product = 0 as well.

Solve : x+1 = 0

Subtract 1 from both sides of the equation :

x = -1

Solve : x-3 = 0

Add 3 to both sides of the equation :

x = 3

Answer 2

Explanation:

4x2 - 8x -12 = 0

divide through by 4

x2 - 2x - 3 = 0

x2 - 3x + x - 3 = 0

(x2 - 3x) + (x - 3) = 0

x(x - 3) + 1(x - 3) = 0

(x + 1) (x - 3) = 0

x + 1 = 0 and x - 3 = 0

x = -1 and x = 3