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<-6` and
`x>-4`, and that
`x^2+10x+24<0` when
`-6<x<-4`.

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