Question

A polynomial of degree n has

Answer 1

The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots (counting multiplicity). ... To get from "at most" to "exactly" you need a way to show that a polynomial of degree n has at least one root. Then you can proceed by induction.

Answer 2

The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots (counting multiplicity). ... To get from "at most" to "exactly" you need a way to show that a polynomial of degree n has at least one root. Then you can proceed by induction.

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