Find a polynomial function with integer coefficients that hasthe given zeros: 1, 5i, -5i

Graham Beasley

Graham Beasley

Answered question

2022-07-28

Find a polynomial function with integer coefficients that hasthe given zeros:
1, 5i, -5i

Answer & Explanation

juicilysv

juicilysv

Beginner2022-07-29Added 17 answers

Since the zeroes are 1, 5i and -5i, these can be obtained by the following conditions:x-1=0 and x 2 + 25 = 0 (as "i" in "5i" is an imaginary number).
Therefore, the required polynomial function can be obtained bymultiplying these two conditions:
( x 1 ) ( x 2 + 25 ) which is actually
x 3 x 2 + 25 x 25
Hayley Bernard

Hayley Bernard

Beginner2022-07-30Added 5 answers

Let's start with the imaginary roots.
( x 5 i ) ( x + 5 i ) = x 2 + 25
We now multiply this to (x-1).
( x 2 + 25 ) ( x 1 ) = x 3 x 2 + 25 x 25
Polynomial function: x 3 x 2 + 25 x 25

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