SOLUTION: Solve x^3 - x^2 - 7x +15 =0 over the set of complex numbers

Question 312825: Solve x^3 - x^2 - 7x +15 =0 over the set of complex numbers
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

First apply the Rational Root Theorem. The possible rational roots of:

are any rational number of the form

where

and

is a factor of

and

is a factor of

Your lead coefficient being 1 simplifies things a little...your possible rational roots are:

Use Synthetic Division and the Remainder Theorem to determine if any of these 8 possibilities are actually roots of the given equation.

If you are unfamiliar with the process of synthetic division, check out Purple Math's explanation at http://www.purplemath.com/modules/synthdiv.htm.

The Remainder Theorem says that the remainder when you use synthetic division with a divisor of

is equal to

, and if

, then

must be a root of

Fortunately for this particular problem, one of the rational roots actually works. When you find the correct synthetic divisor, you will be left with the coefficients of a quadratic equation that can be solved with the quadratic formula to yield a conjugate pair of complex roots.

John

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