Alyssa N.

asked • 01/30/20

Find complex roots for 2x^5 + x^3 - 5x^2 + x + 8 = 0

Find complex roots for 2x^5 + x^3 - 5x^2 + x + 8 = 0

then

factor completely over the set of integers

x^3 -7x^2 + 36

Mark M.

Check the first equation. It has only one real root, -0.956164.
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01/31/20

Nate T.

Mark, I believe it also has 4 complex roots
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01/31/20

Paul M.

tutor
I agree with both Nate & Mark. The root Mark notes cannot be found in closed form. In addition I am not aware of a way to find complex roots unless the real roots can be computed in closed form and then the complex roots must be able to be defined by factoring, i.e. I don't know of a way to find complex roots with coefficients which cannot be defined in closed form.
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01/31/20

Paul M.

tutor
Oops, I forgot: Of course you can get the complex roots of a quartic! There is a complicated but, nevertheless, general formula which will give the roots of a quartic...but if the real root can only be computed numerically, then the general quartic formula will only give approximate values since dividing out the real root will only give approximate coefficients for the quartic.
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01/31/20

1 Expert Answer

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Mark H. answered • 02/05/20

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factor completely over the set of integers

x^3 -7x^2 + 36

Using either long division or synthetic division, find the first factor---I just use trial and error for this. Divide the expression by the first factor to get a quadratic equation, then factor that


I get (x+2)(x-6)(x-3)

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