Question

State whether the following statement is True or False.

If $\text{'}a\text{'}$ is a zero of a polynomial $p\left(x\right)$, then $p\left(a\right)=0$.

• A. True
• B. False

Answer 1

The correct option is A True

Consider $p\left(x\right)=x^3-2x-4$.

1. $p\left(2\right)=2^3-2\times 2-4=0$

Thus, 2 is a zero of the above polynomial.

2. $p\left(1\right)=1^3-2\times 1-4=-5$

Thus, 1 is not a zero of the above polynomial.

Hence, if $\text{'}a\text{'}$ is a zero of a polynomial $p\left(x\right)$, then $p\left(a\right)=0$.

Hence, the given statement is True.