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

Dec 16, 2021

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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

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