sir,there is a statement in my book which i cant understand:
"In fact, a non zero constant polynomial has no zero. what about the zeroes of the zero polynomial?by conversion,every real number is zero of the zero polynomial".

Asked by Umar | 3rd Jul, 2014, 10:50: AM

Expert Answer:

Lets assume Syntax error from line 1 column 59 to line 1 column 90. Unexpected 'P'. , if A=B=C= 0 then the expression becomes zero polynomial.

So zero polynomial can be written as P(X) = 0. For all values of X, we still have root (zero) for zero polynomial.

So every real number is zero of the zero polynomial. Zero of a polynomial is also known as root of polynomial.

Where as when A=B=0 and C is not equal to zero then it is said to be constant polynomial which can be represented as P(X) = k where k is not equal to zero. In this case for any value of X we cannot get zero for the polynomial. So non zero constant polynomial doesn't have roots or Zeros

Definition: The constant polynomial whose coefficients are all equal to 0. The zero polynomial is the additive identity of the additive group of polynomials.

The degree of the zero polynomial is undefined

Answered by Dharma Teja | 7th Jul, 2014, 11:18: AM