Question

Choose the correct statement(s).

i) A linear polynomial has only one zero.
ii ) A quadratic polynomial will have two zeroes.
iii) A quadratic polynomial can have a maximum of two zeroes.
iv) A cubic polynomial can have a maximum of three zeroes.

• A. (ii) only
• B. (i),(iii) and (iv)
• C. (i),(ii) and (iv)
• D. (ii) only

Answer 1

The correct option is B

(i),(iii) and (iv)

A polynomial with degree $n$ can have a maximum of $n$ zeroes.

The degree of a linear polynomial is 1. Thus, a linear polynomial can have one zero at the most.

But if we see a linear polynomial, it's of the form $ax+b,a\ne 0$

The zero of this polynomial will be $x=-\frac{b}{a}$. Since $a\ne 0,-\frac{b}{a}$ is always a real number.

Hence, a linear polynomial will have one zero.

A quadratic polynomial can have a maximum of two zeroes. But this doesn't mean that a quadratic polynomial will have two zeroes.

Similarly, a cubic polynomial can have a maximum of three zeroes.