Question

Find the zeros of f(x)=x4-100

Answer 1

Here, I'll do a similar example:
\(\large\color{black}{ f(x)=x^4-25}\)

\(\large\color{black}{ 0=x^4-25}\)

\(\large\color{black}{ 0\color{red}{+25}=x^4-25 \color{red}{+25} }\)

\(\large\color{black}{ 25=x^4 }\)

you can first take a square root of both sides:

\(\large\color{black}{ \pm 5=x^2 }\)

then take a square root again:

\(\large\color{black}{ - 5=x^2 ~~~\Longrightarrow~~~x=\pm i\sqrt{5}}\)
\(\large\color{black}{ 5=x^2 ~~~~~~\Longrightarrow~~~x=\pm \sqrt{5}}\)

so the zeros are: \(\large\color{black}{ \sqrt{5},~~-\sqrt{5},~~~~~ i\sqrt{5},~~-i\sqrt{5}}\)

Answer 2

@americavera do you have any questions?