Find a polynomial function with integer coefficients that hasthe given zeros:

1, 5i, -5i

1, 5i, -5i

Graham Beasley
2022-07-28
Answered

Find a polynomial function with integer coefficients that hasthe given zeros:

1, 5i, -5i

1, 5i, -5i

You can still ask an expert for help

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

${x}^{3}-{x}^{2}+25x-25$

Therefore, the required polynomial function can be obtained bymultiplying these two conditions:

$(x-1)({x}^{2}+25)$ which is actually

${x}^{3}-{x}^{2}+25x-25$

Hayley Bernard

Answered 2022-07-30
Author has **5** answers

Let's start with the imaginary roots.

$(x-5i)(x+5i)={x}^{2}+25$

We now multiply this to (x-1).

$({x}^{2}+25)(x-1)={x}^{3}-{x}^{2}+25x-25$

Polynomial function: ${x}^{3}-{x}^{2}+25x-25$

$(x-5i)(x+5i)={x}^{2}+25$

We now multiply this to (x-1).

$({x}^{2}+25)(x-1)={x}^{3}-{x}^{2}+25x-25$

Polynomial function: ${x}^{3}-{x}^{2}+25x-25$

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3. Is

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