Find the P(x) polynomial of the smallest degree possible, with zeros 2 + i, and -3, such that -3 is a zero of multiplicity of 2 and P(-1)=2. Expand your polynomial completely.

Rohan Mcpherson

Rohan Mcpherson

Answered question

2022-10-06

Find the P(x) polynomial of the smallest degree possible, with zeros 2 + i, and -3, such that -3 is a zero of multiplicity of 2 and P(-1)=2. Expand your polynomial completely.

Answer & Explanation

Alannah Hanson

Alannah Hanson

Beginner2022-10-07Added 11 answers

P(x) be apolynomial of the smallest degree 2+i is a zero of P(x)
( 2 i ) is also a zero of p(x)
Also -3 is a zero of p(x) with multiplicity 2.
p ( x ) = a ( x + 3 ) 2 ( x 2 i ) ( x 2 + i )
Here a is a constant
Given p ( 1 ) = 2 a ( 1 + 3 ) 2 ( 1 2 i ) ( 1 2 + i ) = 2 4 a ( 3 ) 2 i 2 = 2 4 a ( 9 + 1 ) = 2 a = 2 40 = 1 20 P ( x ) = 1 20 ( x + 3 ) 2 ( x 2 i ) ( x 2 + i ) = 1 20 ( x 2 + 6 x + 9 ) ( x 2 4 x + 5 ) = 1 20 ( x 4 + 2 x 3 10 x 2 6 x + 15 )

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?