What is the value of $b+c$ if $x^2+bx+c>0$ only when $x\in (-\infty, -2)\cup(3,\infty)$?
So, if $x^2+bx+c>0$ only when $x\in (-\infty, -2)\cup(3,\infty)$, that means the roots of the quadratic are $x=-2$ and $x=3$. I can use this information to find $b$ and $c$, since I know that the sum of the roots is equal to $-b/a$ and the product of the roots is equal to $c/a$, where $a$ is the leading coefficient of the quadratic. In this case, $a=1$, so I can simplify these formulas to $-2+3=-b$ and $-2\cdot 3=c$. Solving for $b$ and $c$, I get $b=-1$ and $c=-6$. Therefore, the value of $b+c$ is $-1+(-6)=-7$. 