SOLUTION: Let p(x) =x^5 - 10x^2 + 15x -6 X=1 is a root of p(x) of multiplicity 3. Find the two complex roots of p(x)

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Question 1142739: Let p(x) =x^5 - 10x^2 + 15x -6
X=1 is a root of p(x) of multiplicity 3. Find the two complex roots of p(x)
Answer by josgarithmetic(39627) About Me  (Show Source):
You can put this solution on YOUR website!
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X=1 is a root of p(x) of multiplicity 3.
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Meaning is one of the factors of p is x%5E3-3x%5E2%2B3x-1.

Use polynomial division to find %28x%5E5+-+10x%5E2+%2B+15x+-6%29%2F%28x%5E3-3x%5E2%2B3x-1%29 and analyze the resulting quadratic the way you know or want. You should find the resulting quadratic of the division is x%5E2%2B3x%2B6.

Quadratic Formula Solution gives zeros:
%28-3%2B-+i%2Asqrt%2815%29%29%2F2