Find the Roots (Zeros) f(x)=(x^2+6)^2

$f (x) = {(x^{2} + 6)}^{2}$

Step 1

Set ${(x^{2} + 6)}^{2}$ equal to $0$ .

${(x^{2} + 6)}^{2} = 0$

Step 2

Solve for $x$ .

Set the $x^{2} + 6$ equal to $0$ .

$x^{2} + 6 = 0$

Solve for $x$ .

Subtract $6$ from both sides of the equation.

$x^{2} = - 6$

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

$x = \pm \sqrt{- 6}$

Simplify $\pm \sqrt{- 6}$ .

Rewrite $- 6$ as $- 1 (6)$ .

$x = \pm \sqrt{- 1 (6)}$

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$x = \pm \sqrt{- 1} \cdot \sqrt{6}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \pm i \sqrt{6}$

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.

$x = i \sqrt{6}$

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

$x = - i \sqrt{6}$

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

$x = i \sqrt{6}, - i \sqrt{6}$

Step 3