SOLUTION: Hello, I am stumped on the following question. Appreciate the help. Solve x^3-4x^2-2x+20=0 over the set of complex numbers.

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Question 222298: Hello,
I am stumped on the following question. Appreciate the help.
Solve x^3-4x^2-2x+20=0 over the set of complex numbers.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Start with the rational root theorem. The possible rational roots are all where is an integer factor of the constant term and is an integer factor of the high-order term. That means that the possible rational roots for:



are



Next you need to use synthetic division to determine which of the 12 possible rational zeros are actually zeros. If you need a tutorial on synthetic division, Purplemath has a very good one at http://www.purplemath.com/modules/synthdiv.htm

I'm going to take a shortcut here and tell you that -2 is a zero, hence is a factor of and dividing by leaves a quotient of

So now we have



Leaving us with having to solve



which does not factor so we need to use the quadratic formula











Therefore the three roots of:



are , , and

John
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