Question

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

• A. $p\left(\alpha \right)=0$
• B. $p\left(\alpha \right)=1$
• C. $p\left(\alpha \right)=x$
• D. $p\left(\alpha \right)=\alpha$

Answer 1

The correct option is A $p\left(\alpha \right)=0$

Any real number $\alpha$ is said to be a zero of polynomial $p\left(x\right)$ if $p\left(\alpha \right)=0.$

Zero can be seen as the value of $x$ for which the polynomial takes the value as zero.

So, if $x^2-2x+1$ is a polynomial, we know at $x=1.$

In this case, the value of $x^2-2x+1=0,$ hence $x=1$ can be said as zero of $x^2-2x+1$

Hence, the answer is $p\left(\alpha \right)=0.$

That is, option $A$ is correct.