Question

Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and their coefficients.

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

• A. $\sqrt{2},\frac{3}{2}$
• B. $\sqrt{2},\frac{1}{2}$
• C. $\sqrt{2},\frac{7}{2}$
• D. $\sqrt{2},\frac{9}{2}$

Answer 1

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

Given quadratic polynomial is $2s^2-(1+2\sqrt{2})s+\sqrt{2}$

$=2s^2-s-2\sqrt{2}s+\sqrt{2}$

$=s(2s-1)-\sqrt{2}(2s-1)$

$=(2s-1)(s-\sqrt{2})$

$s=\frac{1}{2}$ and $s=\sqrt{2}$

The relationship between the zeroes and their coefficient,

Sum of the zeroes$=-\frac{coefficientofs}{coefficientof{s}^2}$

$=-\left(\frac{-(1+2\sqrt{2})}{2}\right)$

$=\frac{1+2\sqrt{2}}{2}$

Also sum of the zeroes$=\frac{1}{2}+\sqrt{2}$

$=\frac{1+2\sqrt{2}}{2}$

Product of the zeroes$=\frac{constantterm}{coefficientof{s}^2}$

$=\frac{\sqrt{2}}{2}$

Also product of the zeroes$=\frac{1}{2}\times \sqrt{2}$

$=\frac{\sqrt{2}}{2}$

Hence verified.

$OptionBiscorrect$