SOLUTION: For the quadratic fucntion Q(x) = x^2+5x-36, determine the x-intercept(s).

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Question 89201: For the quadratic fucntion Q(x) = x^2+5x-36, determine
the x-intercept(s).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve x%5E2%2B5%2Ax-36=0 ( notice a=1, b=5, and c=-36)

x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A-36+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=-36



x+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A-36+%29%29%2F%282%2A1%29 Square 5 to get 25



x+=+%28-5+%2B-+sqrt%28+25%2B144+%29%29%2F%282%2A1%29 Multiply -4%2A-36%2A1 to get 144



x+=+%28-5+%2B-+sqrt%28+169+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-5+%2B-+13%29%2F%282%2A1%29 Simplify the square root



x+=+%28-5+%2B-+13%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-5+%2B+13%29%2F2 or x+=+%28-5+-+13%29%2F2

Lets look at the first part:

x=%28-5+%2B+13%29%2F2

x=8%2F2 Add the terms in the numerator
x=4 Divide

So one answer is
x=4



Now lets look at the second part:

x=%28-5+-+13%29%2F2

x=-18%2F2 Subtract the terms in the numerator
x=-9 Divide

So another answer is
x=-9

So our solutions are:
x=4 or x=-9

Notice when we graph x%5E2%2B5%2Ax-36, we get:

+graph%28+500%2C+500%2C+-19%2C+14%2C+-19%2C+14%2C1%2Ax%5E2%2B5%2Ax%2B-36%29+

and we can see that the roots are x=4 and x=-9. This verifies our answer