Question

Form a quadratic equation with rational coefficients, one of whose roots is $\frac{1}{3+2\sqrt{2}}$.

• A. $x^2+6x+1=0$
• B. $x^2-6x+1=0$
• C. $x^2-6x-1=0$
• D. $x^2+6x-1=0$

Answer 1

Answer: (B)

$x^2-6x+1=0$

Given one root $=\frac{1}{3+2\sqrt{2}}=\frac{3-2\sqrt{2}}{9-8}=3-2\sqrt{2}$

As we need quadratic equation with rational coefficients, other root must be conjugate to first root

$\Rightarrow$ Other root $=3+2\sqrt{2}$

$\Rightarrow$ Quadratic equation with $\alpha ,\beta$ roots is $x^2-x(\alpha +\beta )+\alpha \beta =0$

$\Rightarrow$ Required quadratic equation is $x^2-6x+1=0$