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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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-> 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(20879)
(
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