Quadratic inequality

From https://web2.0calc.com/questions/what-is-the-value-of-b-c-if-x-2-bx-c-gt-0-only-when

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.

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