Question

Which of the following given option is/ are NOT correct?

• A. Degree of a zero polynomial is $0$.
• B. Degree of a zero polynomial is not defined.
• C. Degree of a constant polynomial is not defined.
• D. A polynomial of degree n must have $n$ zeroes

Answer 1

Answer: (A), (C), (D)

The correct options are
A Degree of a zero polynomial is $0$.
C A polynomial of degree n must have $n$ zeroes
D Degree of a constant polynomial is not defined.

A polynomial function is a function such as a quadratic, a cubic, a quartic, and so on, involving only non-negative integer powers of x.

$⟹$ A polynomial of degree n is a function of the form :

$f\left(x\right)=a_n{x}^n+a_{n-1}{x}^{n-1}+...a_{1}x+a_0$

The degree of a polynomial is the highest power of the variable.

$⟹$ Degree of a zero polynomial is not defined because the function value never changes or is constant.

$⟹$ Degree of a constant polynomial $f\left(x\right)=c$ is $0$ because we can write it as $f\left(x\right)=c{x}^0$.

$⟹$ ${(x-2)}^2$ is quadratic eqution with degree 2 but has only one zero that is 2.

Hence, A,C and D are not correct.