Tahmid Knox

2021-08-18

Write a third-degree polynomial in standard form with roots x = 4 and x - 2i.
$f\left(x\right)=a(x-4)(x-2i)(x+2i)$

lobeflepnoumni

Skilled2021-08-19Added 99 answers

By expanding,

$f\left(x\right)=a(x-4)({x}^{2}-2ix+2ix+4)$

$f\left(x\right)=a(x-4)({x}^{2}+4)$

$f\left(x\right)=a[{x}^{2}(x-4)+4(x-4)]$

$f\left(x\right)=a({x}^{3}-4{x}^{2}+4x-16)$

For simplicity, use a=1. So, a possible third-degree polynomial is:

$f\left(x\right)=1({x}^{3}-4{x}^{2}+4x-16)$

$f\left(x\right)={x}^{3}-4{x}^{2}+4x-16$

For simplicity, use a=1. So, a possible third-degree polynomial is:

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