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It follows from the Zero Product Property that x=-2, or x2=-1

Solving x2=-1yields two imaginary roots, x=i or x=-i

Graph the related function y=x4-3x2-4=0

The graph shows zeros at x=2 and x=-2

It shows the three turning points. This means that there are imaginary roots, which didn't appear on the graph.

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Extra Credit

By Jack Leonard