Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n=4; 2 i and 3 i are zeros

Nola Aguilar

Nola Aguilar

Answered question

2022-11-19

Find an nth-degree polynomial function with real coefficients satisfying the given conditions
n = 4 2 i  and  3 i  are zeros f ( 1 ) = 100

Answer & Explanation

Hector Hamilton

Hector Hamilton

Beginner2022-11-20Added 13 answers

Given: 2i and 3i are two roots
so -2i and -3i are als two work
so all 4 nuts, 2 i , 2 i , 3 i , 3 i
Let the equation obtainde by roots
f ( x ) = a ( x x 1 ) ( x x 2 ) ( x x 3 ) ( x x 4 ) f ( x ) = a ( x + 2 i ) ( x + 3 i ) ( x 2 i ) ( x 3 i ) f ( x ) = a ( x 2 ( 2 i ) 2 ) ( x 2 ( 3 i ) 2 ) f ( x ) = a ( x 2 + 4 ) ( x 2 + 9 ) f ( 1 ) = 1 f ( x ) = 2 ( x 2 + 4 ) ( x 2 + 9 ) f ( x ) = 2 x 4 + 26 x 2 + 72

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?