Question

What are the zeros of a constant polynomial and a zero polynomial

Answer 1

The constant polynomial P(x)=0 whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. The zero polynomial is the additive identity of the additive group of polynomials.

The degree of the zero polynomial is undefined, but many authors conventionally set it equal to -1 or -infty. In the Wolfram Language, Exponent[0, x] returns -Infinity.

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Answer 2

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• The constant polynomial has coefficients all equal to 0. The zero polynomial is the additive identity (P(x)=0) of the additive group of polynomials.

• A constant polynomial has a degree of 0 and a zero polynomial has an undefined degree