Chapter 9, Problem 24MCQ

To determine

To solve the given equation by factoring.

Answer to Problem 24MCQ

The value of x is -4 and $\frac{3}{2}$ .

Explanation of Solution

Given information :

The equation provided is $2x^2+5x-12=0$ .

Formula used :

The given equation can be solved by factoring. To do so, break up the midpoint to arrive at two factors. Then use the zero-product property to equate each factor in order to get the roots.

Calculation :

  $2x^2+5x-12=0$

Given equation.

  $=>2x^2+8x-3x-12=0$

Breaking the middle term.

  $=>2x\left(x+4\right)-3\left(x+4\right)=0$

Arranging the common factors.

  $=>\left(2x-3\right)\left(x+4\right)=0$

The two factors of the function.

Now, the first root is:

  $2x-3=0$

Using zero-product property.

  $x=\frac{3}{2}$

The second root is:

  $x+4=0$

Using zero-product property.

  $x=-4$

Thus, the values of x are is -4 and $\frac{3}{2}$ .