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(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 :

Given:

[tex]x^4+2x^2-3=0[/tex]

We will find the zeros of the function:

Factor the given function:

[tex]\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}[/tex]

So, there are four zeros

So, the answer will be:

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

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