Try to complete Factorization Factor the polynomial completely , and find all its zeros. State the multiplicity of each zero. P(x)=x^{4}-625

Brittney Lord 2020-10-20 Answered
Try to complete Factorization Factor the polynomial completely , and find all its zeros. State the multiplicity of each zero.
P(x)=x4625
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

SkladanH
Answered 2020-10-21 Author has 80 answers
Concept used:
The multiplicity of zero of the polynomial having factor (xc) that appears k times in the factorization of the polynomial is k.
Calculation:
The given polynomial is P(x)=x4625.
Factor the above polynomial to obtain the zeros
P(x)=x4625
=((x2)2(25)2)
=(x225)(x2+25)
=(x252)(x2(5i)2)
Further factorize the above expression
P(x)=(x252)(x2(5i)2)
=(x+5)(x5)(x+5i)(x5i)
Substitute 0 for P(x) in the polynomial P(x)=x4625 to obtain the zeros of the polynomial.
(x+5)(x5)(x+5i)(x5i)=0
Further solve for the value of x as,
(x+5)=0,(x5)=0,(x+5i)=0 and (x5i)=0
x=5,x=5,x=5i and x=5i
All the zeros in the polynomial P(x)=x4625 appear one times in the polynomial.
Therefore, the multiplicity of zeros 5i, —5i, 5 and —5 is 1.
Conclusion:
Thus, the factorization of the polynomial P(x)=x4625 is
P(x)=(x+5)(x5)(x+5i)(x5i), zeros of the polynomial are ±5 and ±5i and the multiplicity of all the zeros is 1.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more