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

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

Step-by-step 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

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

Step-by-step 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.