Question

True or False Questions

Number of zeroes of a polynomial cannot exceed its degree.

• A. True
• B. False

Answer 1

The correct option is A True

Degree of a polynomial: When the polynomial is in one variable, the highest power of the variable is called the degree of the polynomial.

Zeroes of a polynomial: A real number $a$ is a zero or root of the polynomial $p\left(x\right)$ if $p\left(a\right)=0$.

To find the zero of a polynomial $p\left(x\right)$, we need to solve the polynomial equation $p\left(x\right)=0$. From this, we can find that $n^{th}$degree polynomial can have a maximum number of zeroes equal to its degree.

For example: Let a polynomial $p\left(x\right)=x+5$

Equate the polynomial equal to zero:

Thus, $$\begin{gathered} x+5=0 \\ x=-5 \end{gathered}$$

A linear polynomial (polynomial having degree one) has only one zero. Thus we can conclude that number of zeroes cannot exceed its degree.

Hence, the given statement is True.