# 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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juicilysv
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:
$\left(x-1\right)\left({x}^{2}+25\right)$ which is actually
${x}^{3}-{x}^{2}+25x-25$
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Hayley Bernard
$\left(x-5i\right)\left(x+5i\right)={x}^{2}+25$
We now multiply this to (x-1).
$\left({x}^{2}+25\right)\left(x-1\right)={x}^{3}-{x}^{2}+25x-25$
Polynomial function: ${x}^{3}-{x}^{2}+25x-25$