How do you find all the zeros of #x^5+x^3-30x #?

1 Answer
George C.
Jul 8, 2018

Factor to find zeros:

#0, +-sqrt(5)# and #+-sqrt(6)i#

Explanation:

After separating out the common factor #x#, the remaining quartic can be factored like a quadratic, before reducing to linear factors:

#x^5+x^3-30x = x(x^4+x^2-30)#

#color(white)(x^5+x^3-30x) = x(x^2+6)(x^2-5)#

#color(white)(x^5+x^3-30x) = x(x-sqrt(6)i)(x+sqrt(6)i)(x-sqrt(5))(x+sqrt(5))#

Hence zeros:

#0, +-sqrt(5)# and #+-sqrt(6)i#

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