Question

$\text{Which of the following is a zero of the}\text{polynomial}p\left(x\right)=x^2-4x+4?$

• A. 4
• B. 1
• C. 2
• D. 8

Answer 1

The correct option is C 2

Zero of a polynomial is the point at which the value of polynomial becomes zero.

$\text{If a is a factor of p(x), then from}\text{factor theorem, we have p(a) = 0.}$

$\text{Substituting the options in p(x),}\text{we get;}$
$p\left(4\right)=4^2-4\left(4\right)+4=16-16+4$
$=4\ne 0$
$p\left(1\right)=1^2-4\left(1\right)+4=1-4+4$
$=1\ne 0$
$p\left(2\right)=2^2-4\left(2\right)+4=4-8+4$
$=0$
$p\left(8\right)=8^2-8\left(4\right)+4=64-32+4$
$=36\ne 0$

Here the value of polynomial P(x) becomes zero at x = 2.
$\text{Hence, 2 is the zero of the polynomial}{x}^2-4x+4$.