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`

Step-by-step 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}`