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

Graham Beasley 2022-07-28 Answered
Find a polynomial function with integer coefficients that hasthe given zeros:
1, 5i, -5i
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Answers (2)

juicilysv
Answered 2022-07-29 Author has 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
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Hayley Bernard
Answered 2022-07-30 Author has 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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