# How do you find all real zeros of the function f(x)=2x(x-9)^2(x-2)^2?

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#### Explanation

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#### Explanation:

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Alan P. Share
Jan 10, 2017

Real zeros at $x \in \left\{0 , 9 , 2\right\}$

#### Explanation:

As an explicit expansion can be factored as:
$f \left(x\right) = \textcolor{red}{\text{(2x))xxcolor(blue)(""(x-9))xxcolor(green)(""(x-9))xxcolor(orange)(""(x-2))xxcolor(magenta)(} \left(x - 2\right)}$

Each factor gives one (not necessarily unique) zero:
{: ("factor:",color(red)(""(2x)),color(blue)(""(x-9)),color(green)(""(x-9)),color(orange)(""(x-2)),color(magenta)(""(x-2))), ("implied zero:",color(white)("X")color(red)0,color(white)("X")color(blue)9,color(white)("X")color(green)9,color(white)("X")color(orange)2,color(white)("X")color(magenta)2) :}

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