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The question is "Draw a graph that possibly represents the following situation: A 7th degree polynomial equation with 4 imaginary roots." How would I draw this graph?

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2 Answers

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Hint: Draw a graph of a polynomial with exactly $7$ real roots, and the usual maxima/minima between roots. Then shift the $x$-axis upwards/downwards so that $4$ of the real roots disappear.

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Here is one example. The roots for $f(z)$ are $1,5,9,2+i3,2-i3,7+i4,7-i4$.

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