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±√b2−4ac2a=−1±√12−4(1)(1)2(1)=−1±√−32=−1±√3i2
So the zeros of P are 0,−1+√3i2 and −1−√3i2.
b.) By complete factorization,
P(x)=(x)[x−(−1+√3i2)][x−(−1−√3i2)]=x[x+(1−√3i2)][x+(1+√3i2)]
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