Complete Factorization Factor the polynomial completely, and find all its zeros.State the multiplicity of each zero. P(x) = x^{4}+2x^{2}+1

Rui Baldwin

Rui Baldwin

Answered question

2020-11-09

Complete Factorization Factor the polynomial completely, and find all its zeros.State the multiplicity of each zero.
P(x)=x4+2x2+1

Answer & Explanation

2abehn

2abehn

Skilled2020-11-10Added 88 answers

Concept used:
The multiplicity of zero of the polynomial having factor (x — c) that appears k times in the factorization of the polynomial is k.
Calculation:
The given polynomial is P(x)=x4+2x2?+1.
Factor the above polynomial to obtain the zeros.
P(x)=x4+2x2+1=((x2)2+21x+1)
=(x2+1)2=(x2+1)(x2+1)
P(x)=(x2+1)(x2+1)
=(x2i2)(x2i2)
=(x+i)(xi)(x+i)(xi)
Substitute 0 for P (x) in the polynomial P(x)=x4+2x2+1 to obtain the zeros of the polynomial.
(x+i)(xi)(x+i)(xi)=0
Further solve for the value of x as,
(xi)=0 and (x+i)=0
x=i and x=i
All zeros of the polynomial P(x)=x4+2x2+1 appears two times in the polynomial therefore, the multiplicity of zeros -i, and i is 2.
Conclusion:
Thus, the factorization of the polynomial P(x)=x4+x2+1 is P(x)=(xi)2(x+i)2,zeros of the polynomial are +i and the multiplicity of the zeros is 2.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?