Question

Solve the following equation by factoring: 2x^2-5x-12=0

Answer choices:
A.x=-4 or x=-3/2
B.x=-4 or x=3/2
C.x=3/2 or x=4
D.x=-3/2 or x=4

Answer 1

D. x=-3/2 or x=4

Explanation:

To solve this, factor the equation 2x^2-5x-12. Since -12 is negative, one of the factors has to be negative and one has to be positive. Since the coefficient of x is -5, 1 times a factor plus 2 times another factor has to sum to -5. Trying factors, we realize that (2x+3)(x-4)=0 works. Solving, 2x+3=0 and x-4=0, or x=-3/2 or x=4.

Answer 2

D.x=-3/2 or x=4

Explanation:

2x^2-5x-12=0

Factor

(2x +b ) (x+a ) =0

We need to get -12

Choices

-1 *12 -2 *6 -3*4 -4*3 -6*2 - 12*1

The first number is 2 because the x^2 coefficient is 2

2 * a +b = -5

Let a = -4 and b = 3

2*-4 +3 = -5

(2x +3)(x-4) =0

Using the zero product property

2x+3 =0 x-4 =0

2x =-3 x=4

x = -3/2