The polynomial of degree 5, P(x) has leading coefficient 1,

Racetovb4j

Racetovb4j

Answered question

2022-02-03

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-3, how do you find a possible formula for P(x)?

Answer & Explanation

bubble53zjr

bubble53zjr

Beginner2022-02-04Added 14 answers

Since each root is a linear factor, we can write:
P(x)=x2(x1)2(x+3) 
=x2(x22x+1)(x+3) 
=x5+x45x3+3x2 
Any polynomial that contains these zeros and at least these multiplicities is going to be a multiple (scalar or polynomial) of this P(x) 
Answer: 
P(x)=x5+x45x3+3x2

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?