Solution assignment 01 Quadratic inequalities

Solve:

$x^2+7x+12\leq0$

First we solve the corresponding equation:

$x^2+7x+12=0$

which can be easily solved by factorizing. We write:

$x^2+7x+12=(x+4)(x+3)=0$

and the solutions are:

$x=-4$ or $x=-3$

The graph of the function in the left-hand side is an 'opens up' parabola, and thus the following values of $x$ satisfy the inequality:

$-4\leq{x}\leq{-3}$