Question

What graph represents the solution for x^2+x-12>0

Answer 1

Explanation:

`x^2+x-12>0\\\\x^2+4x-3x-12>0\\\\x(x+4)-3(x+4)>0\\\\(x+4)(x-3)>0\\\\\text{zeros}\\\\x+4=0\Rightarrow x=-4\\\\x-3=0\Rightarrow x=3`

Mark the zeros on a number line. Draw a parabola open up that goes through zeros.

We are looking for numerical intervals in which the parabola has positive values ​​(graph above the axis).

(look at the picture)

`x^2+x-12\iff x\in(-\infty,\ -4)\ \cup\ (3,\ \infty)`