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Solve the polynomial equation check all solutions both real and imaginary (x^2-9)(x^2+4)=0

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We have the next polynomial equation


\mleft(x^2-9\mright)\mleft(x^2+4\mright)=0

First we will solve because if this binomial is zero all the polynomial expression is zero


\mleft(x^2-9\mright)=0


\begin{gathered} x^2=9 \\ x=\pm\sqrt[]{9} \\ x=\pm3 \end{gathered}

the first two solutions are x=3, x=-3

For the second binomial


(x^2+4)=0
\begin{gathered} x^2=-4 \\ x=\pm\sqrt[]{-4} \\ x\pm2i \end{gathered}

the other solutions are x=2i, x=-2i

The solutions of the polynomial equation are

x=3

x=-3

x=2i

x=-2i

User Henry Moshkovich
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