Question

Consider the polynomial:

$a_n{x}^n$ + $a_{n-1}{x}^{n-1}$ + $a_{n-2}{x}^{n-2}$ + ....+$a_{1}x$ + $a_0$

When will this polynomial be called Zero Polynomial?

• A. $a_n=0$
• B. $a_n=a_{n-1}=....a_1=0$
• C. $a_n=a_{n-1}=....a_1=a_0=0$
• D. $a_0=0$

Answer 1

The correct option is C $a_n=a_{n-1}=....a_1=a_0=0$

A polynomial of the form

$a_n{x}^n$ + $a_{n-1}{x}^{n-1}$ + $a_{n-2}{x}^{n-2}$ + ....+$a_{1}x$ + $a_0$

can be called a zero polynomial when

$a_n=a_{n-1}=....a_1=a_0=0$

$\therefore$ $a_n=a_{n-1}=....a_1=a_0=0$ is the required answer