Question

Degree of a zero polynomial is:
$
  (a){\text{ 0}} \\
  (b){\text{ 1}} \\
  (c){\text{ any natural number}} \\
  (d){\text{ not defined}} \\
 $

Answer 1

Hint: The degree of a polynomial is the largest exponent on one of its variables, use this concept along with the basic definition of a zero polynomial to see the largest exponent that will be the answer.

Complete Step-by-Step solution:
The constant polynomial f(x) = 0 or f(x) = c, where c is any arbitrary constant is called zero polynomial.
So, the degree of zero polynomial is not defined.
A polynomial of degree one is called a linear polynomial
For e.g. ax + b, where a ≠ 0.
A polynomial of degree two is called a quadratic polynomial
For e.g. ax2 + bx + c where a ≠ 0.
So the degree of zero polynomial is not defined.
Hence option (D) is correct.

Note: A zero polynomial, also termed as constant polynomial is one 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 the polynomials.