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What is the value of b+c if x^2+bx+c>0 only when x is in (-inf, -2) U (8, inf)?

 Jun 14, 2021

Best Answer 

 #1
avatar+2135 
+2

Let's rewrite (x+m)(x+n) as x^2+bx+c. 

This will be positive when x + m and x + n are both positive, or both negative. 

This means that at 8, x + m will be 0, and at -2, x + m will be 0. 

(x - 8)(x + 2) = x^2 - 6x - 16

-6 - 16 = -22

 

=^._.^=

 Jun 14, 2021
 #1
avatar+2135 
+2
Best Answer

Let's rewrite (x+m)(x+n) as x^2+bx+c. 

This will be positive when x + m and x + n are both positive, or both negative. 

This means that at 8, x + m will be 0, and at -2, x + m will be 0. 

(x - 8)(x + 2) = x^2 - 6x - 16

-6 - 16 = -22

 

=^._.^=

catmg Jun 14, 2021

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