Question

(Pre-cal polynomial functions) When I'm finding the zeros of x^4 + 2x^2 - 3, how do I know when to implement imaginary numbers for the answer? ( +- [root3] vs. +- i[root3] ).

Answer 1

Given:

`x^4+2x^2-3=0`

We will find the zeros of the function:

Factor the given function:

`\begin{gathered} (x^2+3)(x^2-1)=0 \\ x^2-1=0\rightarrow x^2=1\rightarrow x=\pm1 \\ x^2+3=0\rightarrow x^2=-3\rightarrow x=\pm i\sqrt[]{3} \end{gathered}`

So, there are four zeros

So, the answer will be:

`x=\mleft\lbrace-1,1,i\sqrt[]{3},-i\sqrt[]{3}\mright\rbrace`