Exercise 2.

What can you say about the degree of the polynomial f(x) depicted below?

Answer.

The graph has at least three x-intercepts, thus f(x) has at least three real roots. Consequently, f(x) has at least degree 3.

You can't see complex roots in a graph of a polynomial, so the graph does not provide any information about the number of complex roots.

Indeed, the graph depicted is the graph of the degree-7 polynomial

displaymath27

The polynomial has three real roots and four complex roots.

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Helmut Knaust
Sun Jun 8 21:50:33 MDT 1997

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