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

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Jan 19, 2019

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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

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

Jan 20, 2019