SOLUTION: find all of the other roots of the polynomial equation x^5-x^3-8x^2+8=0

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Question 129562This question is from textbook algebra 2
: find all of the other roots of the polynomial equation x^5-x^3-8x^2+8=0 This question is from textbook algebra 2

Answer by chitra(359) About Me  (Show Source):
You can put this solution on YOUR website!
+graph%28+500%2C+500%2C+-30%2C+30%2C+-30%2C+30%2C+x%5E5+-+x%5E3+-8x%5E2+%2B+8%29+

by observing the graph we cn find that -1 and +1 are the first twoo roots.
The other 3 roots are repeated roots and it would be 2.

This can be factorised by the method of trail and error method and then by synthetic division method.

by the trail and error method we find that 1 is the first factor

%28x+-+1%29%28x%5E4+%2B+x%5E3+-+8x+-+8%29

Then the second equation is agin siplified

here we find that x + 1 is a factor.

So %28x+-+1%29%28x+%2B+1%29%28x%5E3+-+8%29+ will be the next eqn.


So the last eqn will be %28x%5E3+-+8%29 can be factored and thus we get repeated roots

hence, the roots are x = 1, -1, 2, 2, 2

(x - 1)(x + 1)(x- 2)(x - 2)(x - 2)

Are the roots of the eqn

Thus the solution

Regards
Chitra