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What is a polynomial of degree n has at the most?

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Final answer:

A polynomial of degree n can have at most n roots.

Step-by-step explanation:

A polynomial of degree n can have at the most n real roots, which correspond to the x-intercepts on a graph of the function.

Additionally, the polynomial can have at most n-1 turning points, which are the locations on the graph where the function changes direction from increasing to decreasing, or vice versa.

It's crucial to understand that while a polynomial may have up to n real roots, some of the roots could be complex numbers, and in that case, there would be fewer than n x-intercepts.

An example to illustrate this would be a quadratic polynomial (which is of degree 2); it can have up to 2 real roots or a single real root if the discriminant is zero.

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