Question

Find the zeros of polynomial function. f(x)=x^2-x-90

Answer 1

First step is to factor. With a polynomial function in the form ax² + bx + c = f(x), we have to find what factors of term C have a sum of term B.

So with this, we need factors of -90 add up to become -1. Your factors are - 10 and 9.

f(x) = x² + 9x - 10x - 90

Now we group together and pull out GCFs.

f(x) = (x² + 9x) + (10x - 90)

f(x) = x(x² + 9) - 10(x + 9)

f(x) = (x - 10)(x + 9)

Now, set each factor equal to zero.

x - 10 = 0, x + 9 = 0

For the first equation you are going to add 10 to both sides to get x by itself. Subtract 9 from both sides in the second equation for the same reason.

x = 10, x = -9

Your zeros are at x = -9, 10 or at the ordered pairs (-9, 0) and (10, 0).