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What is the value of b + c if x^2 + bx + c > 0 only when x is less than -4 or x is greater than 8?

 Nov 4, 2020
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The graph of  y = x2 + bx + c  is a parabola that opens upward and intersects the x-axis at  -4  and  8 .

 

An equation for a parabola that opens upward and intersects the x-axis at  -4  and  8  is  y = (x + 4)(x - 8)

 

Let's take the second equation and expand the right side by FOILing it:

 

y  =  (x + 4)(x - 8)

 

y  =  x2 - 4x - 32

 

Now we can see that  x2 - 4x - 32  matches  x2 + bx + c  and so we can say...

 

b = -4

c = -32

 

b + c = -36

 

Here's a graph of that parabola expressed both ways: https://www.desmos.com/calculator/afkj6kil8d

 Nov 4, 2020

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