Question

Find the zeroes of the following polynomial by factorisation method:

$2s^2-(1+2\sqrt{2})s+\sqrt{2}$.

• A. $\frac{1}{2},\sqrt{2}$
• B. $\frac{1}{2},2$
• C. $\frac{1}{\sqrt{2}},\sqrt{2}$
• D. None of the above

Answer 1

The correct option is A $\frac{1}{2},\sqrt{2}$

Given, $2s^2-(1+2\sqrt{2})s+\sqrt{2}$
$=2s^2-s-2\sqrt{2}s+\sqrt{2}$
$=s(2s-1)-\sqrt{2}(2s-1)$
$=(2s-1)(s-\sqrt{2})$.

So, the zeros of the polynomial are
$(2s-1)=0$ and $(s-\sqrt{2})=0$
That is, $s=\frac{1}{2}$ and $s=\sqrt{2}$.

Therefore, option $A$ is correct.