Question

The polynomial $a{x}^2+bx+c$ is a linear polynomial if

• A. a = 0
• B. b = 0
• C. both a=0, b=0
• D. neither a=0 nor b=0

Answer 1

The correct option is A

a = 0

A linear polynomial must be of the form $ax+b$ where $a\ne 0$.
The degree of the given polynomial $a{x}^2+bx+c$ is 2, when $a\ne 0$.
When $a=0$ the polynomial reduces to the form $bx+c$ and will be a linear polynomial
But when $a=0andb=0$ the polynomial will be of the form $c$ which is a constant.
Thus, when $a=0andb\ne 0$, $a{x}^2+bx+c$ will be a linear polynomial.