find all real and imaginary solutions of f(x) = x^3 + x^2 + 13x -15

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- Mar 20th 2010, 08:16 PMkenzie103109real and imaginary solutions
find all real and imaginary solutions of f(x) = x^3 + x^2 + 13x -15

- Mar 20th 2010, 08:21 PMProve It
You should be able to see that $\displaystyle f(1) = 1^3 + 1^2 + 13(1) - 15 = 0$.

So by the remainder and factor theorems, that means $\displaystyle x - 1$ is a factor.

By using long division:

$\displaystyle x^3 + x^2 + 13x - 15 = (x - 1)(x^2 + 2x + 15)$.

Now use the Quadratic Formula on the Quadratic factor to find the imaginary solutions.