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?

Guest Nov 4, 2020

#1**0 **

The graph of y = x^{2} + 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 = x^{2} - 4x - 32

Now we can see that x^{2} - 4x - 32 matches x^{2} + 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

hectictar Nov 4, 2020