Question

If $p\left(x\right)=x^2-2\sqrt{2}x+1$, then $p\left(2\sqrt{2}\right)$ is equal to

• A. $0$
• B. $1$
• C. $4\sqrt{2}$
• D. $8\sqrt{2}+1$

Answer 1

The correct option is B

$1$

Find the value of $p\left(2\sqrt{2}\right)$

Given expression is

$p\left(x\right)=x^2-2\sqrt{2}x+1$

To obtain $p\left(2\sqrt{2}\right)$, let us substitute $x=2\sqrt{2}$,

$$\begin{gathered} p\left(2\sqrt{2}\right)={\left(2\sqrt{2}\right)}^2-2\sqrt{2}\times 2\sqrt{2}+1 \\ =\left(4\times 2\right)-4\times 2+1 \\ =8-8+1 \\ =1 \end{gathered}$$

Hence $p\left(2\sqrt{2}\right)$ is equal to $1$ and therefore option (B) is correct.