How do you find all zeros of the function $f (x) = x^{3} {(x - 2)}^{2}$ $f(x)=x^3(x-2)^2$ ?

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Answer 1 · 2016-02-26T21:30:23

$x = 0, 2$ $x=0,2$

To find all the zeros of the function, set each factor to $0$ $0$ and solve for $x$ $x$ .

In your case:

$x^{3} = 0$ $x^3=0$
$x = \sqrt[3]{0}$ $x=root(3)(0)$
$x = 0$ $color(green)(x=0)$

$x - 2 = 0$ $x-2=0$
$x = 2$ $color(green)(x=2)$

You can see this holds true graphically as well:

graph{x^3(x-2)^2 [-5, 5, -2.5, 2.5]}

$:.$ , the zeros of the function are $x=0$ and $x=2$ .

How do you find all zeros of the function f(x)=x^3(x-2)^2f(x)=x3(x−2)2f(x)=x^3(x-2)^2?