Question

which equation is true for $x = -6$ and $x = 2$?$2x^2 - 16x + 12 = 0$$2x^2 + 8x - 24 = 0$$3x^2 - 4x - 12 = 0$$3x^2 + 12x + 36 = 0$

Explanation:

Step1: Use roots to form equation

If $x=-6$ and $x=2$ are roots, then $(x+6)(x-2)=0$. Expand this:
$$(x+6)(x-2)=x^2 + 4x - 12=0$$

Step2: Match to given options

Multiply the equation by 2 to scale:
$$2(x^2 + 4x - 12)=2x^2 + 8x - 24=0$$

Step3: Verify roots (optional check)

For $x=-6$: $2(-6)^2 +8(-6)-24=2(36)-48-24=72-72=0$
For $x=2$: $2(2)^2 +8(2)-24=8+16-24=0$

Answer:

B. $2x^2 + 8x - 24 = 0$