Question

A quadratic equation whose roots are $2+\frac{1}{\sqrt{2}}$ and $2-\frac{1}{\sqrt{2}}$ is:

• A. $x^2-7x+8$ = 0
• B. $2x^2-8x+7$ = 0
• C. $2x^2-7x+8$ = 0
• D. $x^2-8x+7$ = 0

Answer 1

The correct option is B

$2x^2-8x+7$ = 0

Roots are $2+\frac{1}{\sqrt{2}}$ and $2-\frac{1}{\sqrt{2}}$
Sum of roots = $2+\frac{1}{\sqrt{2}}$ + $2-\frac{1}{\sqrt{2}}$ = 4
Product of roots = ($2+\frac{1}{\sqrt{2}}$) x ($2-\frac{1}{\sqrt{2}}$) = 7/2
Quadratic equation when roots are given is,
$x^2-\left(sumofroots\right)x+\left(productofroots\right)=0$$\therefore$ $x^2-4x+(7/2)=0TakingLCM=2weget,2x^2-8x+7=0$
which is the required equation.