SOLUTION: What is the value of b+c if x^2+bx+c>0 only when x (-infinity, -2) U (3,infinity)?

Question 1094006: What is the value of b+c if x^2+bx+c>0 only when x (-infinity, -2) U (3,infinity)?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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What is the value of b+c if x^2+bx+c>0 only when x (-infinity, -2) U (3,infinity)?
~~~~~~~~~~~~~~~~~

The condition means that the given polynomial has the roots -2 and 3.


Then the Vieta's theorem says that  


    a)  b = -(sum of the roots) = -((-2)+3) = -(1) = -1

and


    b)  c = the product of the roots = (-2)*3 = -6.


Thus    b + c = -1 -6 = -7.

Solved.

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