Identify the Zeros and Their Multiplicities f(x)=x^6-3.2

$f (x) = x^{6} - 3.2$

Step 1

Set $x^{6} - 3.2$ equal to $0$ .

$x^{6} - 3.2 = 0$

Step 2

Solve for $x$ .

Add $3.2$ to both sides of the equation.

$x^{6} = 3.2$

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

$x = \pm \sqrt[6]{3.2}$

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

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt[6]{3.2}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt[6]{3.2}$

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

$x = \sqrt[6]{3.2}, - \sqrt[6]{3.2}$

The multiplicity of a root is the number of times the root appears. For example, a factor of ${(x + 5)}^{3}$ would have a root at $x = - 5$ with multiplicity of $3$ .

$x = \sqrt[6]{3.2}$ (Multiplicity of $1$ )

$x = - \sqrt[6]{3.2}$ (Multiplicity of $1$ )

$x = \sqrt[6]{3.2}$ (Multiplicity of $1$ )

$x = - \sqrt[6]{3.2}$ (Multiplicity of $1$ )

Step 3

Identify the Zeros and Their Multiplicities f(x)=x^6-3.2

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