Question

A real number '$\alpha$' is said to be a ................. of the polynomial $p\left(x\right)$, if $p\left(\alpha \right)=0$.

• A. linear
• B. zero
• C. constant
• D. cubic

Answer 1

Answer: (B)

zero

If we replace the value of $x$ by a real number, say $\alpha$ in the polynomial $p\left(x\right)$, such that $p\left(x\right)=0$, i.e. $p\left(\alpha \right)=0$, then we say that, the real number '$\alpha$' is a zero of the polynomial $p\left(x\right)$.

E.g.: Suppose $p\left(x\right)=x-1$.

Here, the real number $1$ is a zero of the given polynomial as $p\left(1\right)=1-1=0$, i.e. $p\left(1\right)=0$.

Hence, we can say that, a real number $\alpha$ is said to be a zero of the polynomial $p\left(x\right)$, if $p\left(\alpha \right)=0$.

That is, option $B$ is correct.