Identify the Zeros and Their Multiplicities x^2(x-100)(x-200)

$x^{2} (x - 100) (x - 200)$

To find the roots/zeros, set $x^{2} (x - 100) (x - 200)$ equal to $0$ and solve.

$x^{2} (x - 100) (x - 200) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{2} = 0$

$x - 100 = 0$

$x - 200 = 0$

Set the first factor equal to $0$ and solve.

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Set the first factor equal to $0$ .

$x^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

The complete solution is the result of both the positive and negative portions of the solution.

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Simplify the right side of the equation.

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Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

$\pm 0$ is equal to $0$ .

$x = 0$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$x - 100 = 0$

Add $100$ to both sides of the equation.

$x = 100$

Set the next factor equal to $0$ and solve.

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Set the next factor equal to $0$ .

$x - 200 = 0$

Add $200$ to both sides of the equation.

$x = 200$

The final solution is all the values that make $x^{2} (x - 100) (x - 200) = 0$ true. The multiplicity of a root is the number of times the root appears.

$x = 0$ (Multiplicity of $2$ )

$x = 100$ (Multiplicity of $1$ )

$x = 200$ (Multiplicity of $1$ )

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