Sunday, December 22, 2019

College Algebra, Chapter 4, 4.5, Section 4.5, Problem 8

a.) Find all zeros of P(x)=x3+x2+x of P, real and complex

b.) Factor P completely.



a.) We first factor P as follows.


P(x)=x3+x2+xGiven=x(x2+x+1)Factor out x


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

Setting x=0, we see that x=0 is a zero. More over, setting x2+x+1=0, by using quadratic formula, we get


x=b±b24ac2a=1±124(1)(1)2(1)=1±32=1±3i2


So the zeros of P are 0,1+3i2 and 13i2.

b.) By complete factorization,


P(x)=(x)[x(1+3i2)][x(13i2)]=x[x+(13i2)][x+(1+3i2)]

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