The quadratic equation whose roots are  $$\frac{1}{\sqrt{2}}$$​ and $$\frac{1}{\sqrt{2}}$$​ is:

Correct option is D

Given:

Given roots of equation =$$\frac{1}{\sqrt{2}}\ and\ \frac{1}{\sqrt{2}}$$​​

Formula Used:

If $$\alpha$$​ and $$\beta$$​ are roots of a equation:

Then equation is given by :$$x^2- (\alpha + \beta)x + (\alpha\beta) = 0$$​​

Solution:

Here we have roots of equation $$\alpha = \frac{1}{\sqrt{2}}\ and\ \beta = \frac{1}{\sqrt{2}}$$​​

Then $$x^2 - \left((\frac{1}{\sqrt{2}}) + (\frac{1}{\sqrt{2}})\right)x + \left((\frac{1}{\sqrt{2}})(\frac{1}{\sqrt{2}})\right) = 0$$​​

​$$x^2 - \left(\frac{2}{\sqrt{2}}\right)x + \left(\frac{1}{2}\right) = 0$$​​

​$$\frac{2x^2 - 2 \sqrt{2}x + 1}{2} = 0$$​​

​$$2x^2 - 2 \sqrt{2}x + 1=0$$​​