Question

Solve the inequality. x2 +10x+24 ≤ 0

Answer 1

$x^2+10x+24=(x+6)(x+4)\le0$

Notice that equality holds when either $x=-6$ or $x=-4$, so these should be included in the solution set.


Now, since the coefficient of the leading term is positive, we know the parabola opens upward, which means we know that $x^2+10x+24>0$ when $x$ and $x>-4$, and that $x^2+10x+24$ when $-6$.

So the solution set is the interval $-6\le x\le-4$.