Identify the Zeros and Their Multiplicities x^4-22x^3+121x^2

$x^{4} - 22 x^{3} + 121 x^{2}$

To find the roots/zeros, set $x^{4} - 22 x^{3} + 121 x^{2}$ equal to $0$ and solve.

$x^{4} - 22 x^{3} + 121 x^{2} = 0$

Factor the left side of the equation.

Tap for more steps…

Factor $x^{2}$ out of $x^{4} - 22 x^{3} + 121 x^{2}$ .

Tap for more steps…

Factor $x^{2}$ out of $x^{4}$ .

$x^{2} x^{2} - 22 x^{3} + 121 x^{2} = 0$

Factor $x^{2}$ out of $- 22 x^{3}$ .

$x^{2} x^{2} + x^{2} (- 22 x) + 121 x^{2} = 0$

Factor $x^{2}$ out of $121 x^{2}$ .

$x^{2} x^{2} + x^{2} (- 22 x) + x^{2} \cdot 121 = 0$

Factor $x^{2}$ out of $x^{2} x^{2} + x^{2} (- 22 x)$ .

$x^{2} (x^{2} - 22 x) + x^{2} \cdot 121 = 0$

Factor $x^{2}$ out of $x^{2} (x^{2} - 22 x) + x^{2} \cdot 121$ .

$x^{2} (x^{2} - 22 x + 121) = 0$

Factor using the perfect square rule.

Tap for more steps…

Rewrite $121$ as $11^{2}$ .

$x^{2} (x^{2} - 22 x + 11^{2}) = 0$

Check the middle term by multiplying $2 a b$ and compare this result with the middle term in the original expression.

$2 a b = 2 \cdot x \cdot - 11$

Simplify.

$2 a b = - 22 x$

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = - 11$ .

$x^{2} {(x - 11)}^{2} = 0$

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

$x^{2} = 0$

${(x - 11)}^{2} = 0$

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

Tap for more steps…

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.

Tap for more steps…

Simplify the right side of the equation.

Tap for more steps…

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.

Tap for more steps…

Set the next factor equal to $0$ .

${(x - 11)}^{2} = 0$

Set the $x - 11$ equal to $0$ .

$x - 11 = 0$

Add $11$ to both sides of the equation.

$x = 11$

The final solution is all the values that make $x^{2} {(x - 11)}^{2} = 0$ true. The multiplicity of a root is the number of times the root appears.

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

$x = 11$ (Multiplicity of $2$ )

Identify the Zeros and Their Multiplicities x^4-22x^3+121x^2

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store