What is the value of $b+c$ if $x^2+bx+c>0$ only when $x\in (-\infty, -2)\cup(3,\infty)$?

What is the value of 

 

\( \text{b+c if }\;\;x^2+bx+c>0\qquad \text{only when }\;\;x\in (-\infty, -2)\cup(3,\infty)?\)

 

Well that means that  y cannot not be  positive for  x in [-2,3]

So the roots are x=-2 and x=3 and it is concave up

so the expression is

\((x+2)(x-3) = x^2-x-6 \)

You can do the addition.