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What is a polynomial function for 5, i, -i?

1 Answer

Sep 19, 2016

$f (x) = x^{3} - 5 x^{2} + x - 5$ $f(x)=x^3-5x^2+x-5$

Explanation:

I have assumed that ${5, i, - i}$ ${5,i,-i}$ are intended to be the zeros of the function.

In this case, the function can be factored as:
$XXX (x - 5) ((x - i) (x + i)$ $color(white)("XXX")(x-5)((x-i)(x+i)$

$XXX = (x - 5) (x^{2} - i^{2})$ $color(white)("XXX")=(x-5)(x^2-i^2)$

$XXX = (x - 5) (x^{2} + 1)$ $color(white)("XXX")=(x-5)(x^2+1)$

$XXX = x^{3} + x - 5 x^{x} - 5$ $color(white)("XXX")=x^3+x -5x^x-5$

(or in standard polynomial form)
$XXX = x^{3} - 5 x^{2} + x - 5$ $color(white)("XXX")=x^3-5x^2+x-5$

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