If $$3 + 2\sqrt2$$​ and $$3 - 2\sqrt2$$​ are the roots of a quadratic equation, then the quadratic equation is: 

Correct option is A

Given:

The roots of the quadratic equation are:

$$\alpha = 3 + 2\sqrt{2}, \quad \beta = 3 - 2\sqrt{2}$$​​

Concept Used:

A quadratic equation with roots α\alphaα and β\betaβ is given by:

​$$x^2 - (\alpha + \beta)x + \alpha \beta = 0$$​​

Solution:

Sum of roots:

​$$\alpha + \beta = (3 + 2\sqrt{2}) + (3 - 2\sqrt{2}) = 6$$​​

Product of roots:

​$$\alpha \beta = (3 + 2\sqrt{2})(3 - 2\sqrt{2})$$​​

Using the identity $$(a + b)(a - b) = a^2 - b^2:$$​​

​$$\alpha \beta = 3^2 - (2\sqrt{2})^2 = 9 - 8 = 1$$​​

The quadratic equation is:

​$$x^2 - (\alpha + \beta)x + \alpha \beta = 0$$​​

​$$x^2 - 6x + 1 = 0$$​​