Question

Hi, can you help to find (all the roots) solving this polynomial functions, please!!!

Answer 1

$(x^2_{}+2)^2=0$Given:

There are given the equation:

$x^4+4x^2+4=0$

Explanation:

To find the roots, first, we need to solve the given equation:

So,

From the equation:

$\begin{gathered} x^4+4x^2+4=0 \\ (x^2_{}+2)^2=0 \end{gathered}$

Then,

$\begin{gathered} (x^2_{}+2)^2=0 \\ x^2+2=0 \\ x^2=-2 \\ x=\pm i\sqrt[]{2} \end{gathered}$

Then,

$\begin{gathered} x=\pm i\sqrt[]{2} \\ x=i\sqrt[]{2},-i\sqrt[]{2} \end{gathered}$

Final answer:

Hence, the roots of the given equation are shown below:

$x=i\sqrt[]{2},-i\sqrt[]{2}$