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How do you write a polynomial function in standard form with Zero: 0, multiplicity 2?

1 Answer

May 11, 2016

$f (x) = x^{2}$ $f(x)=x^2$ is one function that meets the specified requirements.

Explanation:

If $f (x)$ $f(x)$ has a multiplicity of 2 then for every value in the range for $f (x)$ $f(x)$ there should be 2 solutions.

Note that this would be true for $f (x) = x^{2}$ $f(x)=x^2$ since if $a$ $a$ is a value in the range for $f (x)$ $f(x)$ then there are 2 solutions for $x$ $x$ , namely $x = - \sqrt{a}$ $x=-sqrt(a)$ and $x = + \sqrt{a}$ $x=+sqrt(a)$

Note that if $f (x)$ $f(x)$ has a zero at $x = 0$ $x=0$
then $f (0) = 0$ $f(0)=0$
and again this will be true for $f (x) = x^{2}$ $f(x)=x^2$

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$f (x) = x^{2}$ $f(x)=x^2$ is not the only possible function meeting the requirements,
in fact
$XXX f (x) = k \cdot x^{2}$ $color(white)("XXX")f(x)=k*x^2$ for any integer value $k$ $k$ will also work.

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