3rd December 2019

teacherschoice
14

How many zeros does a polynomial of degree n have?

The polynomial function y = x4 + 3x3 - 9x2 - 23x - 12 graphed above, has only three zeros, at 'x' = -4, -1and 3. This is one less than the maximum of four zeros that a polynomial of degree four can have.

Just so, what is the maximum number of zeros in a cubic polynomial?

Regardless of odd or even, any polynomial of positive order can have a maximum number of zeros equal to its order. For example, a cubic function can have as many as three zeros, but no more. This is known as the fundamental theorem of algebra.

How do you know how many real roots a polynomial has?

Total Number of Roots. On the page Fundamental Theorem of Algebra we explain that a polynomial will have exactly as many roots as its degree (the degree is the highest exponent of the polynomial). So we know one more thing: the degree is 5 so there are 5 roots in total.
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