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

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

Step 1

Set $x^{2} (x - 100) (x - 200)$ equal to $0$ .

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

Step 2

Solve for $x$ .

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 $x^{2}$ equal to $0$ and solve for $x$ .

Set $x^{2}$ equal to $0$ .

$x^{2} = 0$

Solve $x^{2} = 0$ for $x$ .

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

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

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

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

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

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Set $x - 100$ equal to $0$ and solve for $x$ .

Set $x - 100$ equal to $0$ .

$x - 100 = 0$

Add $100$ to both sides of the equation.

$x = 100$

Set $x - 200$ equal to $0$ and solve for $x$ .

Set $x - 200$ 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 $1$ )

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

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

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

Step 3

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

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