Saturday, October 21, 2017

College Algebra, Chapter 4, 4.5, Section 4.5, Problem 6

a.) Find all zeros of P(x)=x5+9x3 of P, real and complex

b.) Factor P completely.



a.) We first factor P as follows.


P(x)=x5+9x3Given=x3(x2+9)Factor out x3


We find the zeros of P by setting each factor equal to :

Setting x3=0, we see that x=0 is a zero. More over, setting x2+9=0, we get x2=9, so x=±3i. So the zeros of P are 0,3i and 3i.

b.) Since the zeros are 0,3i and 3i, by the complex Factorization Theorem P factors as


P(x)=x(x3i)[x(3i)]=x(x3i)(x+3i)

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