Question

Givethe definition of zeros of polynomial and give examples

Answer 1

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Here's your answer...

Zero of polynomial

The value of variable where the polynomial becomes zero is called as zero of polynomial

For example -

Zero of polynomial of x-3

x-3 = 0

x = 3

3 is the zero of polynomial

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Answer 2

A polynomial with the value zero (0) is known as zero polynomial. Actually, the term 0 is itself zero polynomial. It is a constant polynomial whose all the coefficients are equal to 0.

If the coefficients of following form of polynomial:

bnxn+bn−1xn−1+bn−2xn−2+...+b2x2+b1x+b0bnxn+bn−1xn−1+bn−2xn−2+...+b2x2+b1x+b0

are zero, then it will become zero polynomial.

i.e. bn=bn−1=bn−2=...=b0=0bn=bn−1=bn−2=...=b0=0

Hence, the above polynomial would become 0.

Thus, the zero polynomial may be can be written as P(x) = 0.

This polynomial is eventually the additive identity for other polynomials.