Question

$\text{Find the zeroes of the polynomial}{x}^2-2.$

• A. $\sqrt{2}\text{and}-\sqrt{5}$
• B. $4\text{and}3$
• C. $\sqrt{2}\text{and}-\sqrt{2}$
• D. $-5\text{and}2$

Answer 1

The correct option is C

$\sqrt{2}\text{and}-\sqrt{2}$

$\text{To find the zeroes, equate the given}\text{polynomial to zero.}$

$x^2-2=0$

$\text{Using the identity,}{a}^2-b^2=(a+b)(a-b)$

$\Rightarrow (x+\sqrt{2})(x-\sqrt{2})=0$

$\Rightarrow x+\sqrt{2}=0\text{and}x-\sqrt{2}=0$

$\Rightarrow x=-\sqrt{2}\text{and}x=\sqrt{2}$

$\text{Hence, the zeroes are}\sqrt{2},-\sqrt{2}$.