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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)?

 Oct 19, 2022
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What is the value of b+c if x^2+bx+c>0 only when x(,2)(2,)??

 

x2+bx+c>0

 

this is a concave up parabola.

If this function is greater than zero for all values of x except for x=2  then the vertex is  (2,0)

And there will only be one root.

so

x2+bx+c=(x2)2b=4,c=4b+c=0

 Oct 20, 2022

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