Chapter 4.3, Problem 51P

Consider the equation $a{y}^{″}+b{y}^{\prime }+cy=0$, where $a,b,$ and $c$ are constants with $a>0$. Find conditions on $a,b,$ and $c$ such that the roots of the characteristic equation are:

(a) Real, different, and negative.

(b) Real with opposite signs.

(c) Real, different, and positive.