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

 Jul 6, 2023
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What is the value of \(b+c\) if \(x^2+bx+c>0\) only when\(x\in (-\infty, -2)\cup(2,\infty)\)?

 

So this is a parabola that opens up and has x intercepts at (-2,0) and (2,0). The slope is 1. So the equation of the graph is \(x^2-4\). Making b=0 and c=-4, so \(b+c=\boxed{-4}\)

 Jul 6, 2023

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