The quadratic equation whose one root is $$3+\sqrt5$$​, is:

Correct option is B

Given:

One root of the quadratic equation is 3 + $$\sqrt{5}.$$​​

Concept Used:
If one root of the quadratic equation is 3 $$+ \sqrt{5}$$​, the other root will be the conjugate, $$3 - \sqrt{5}$$​,

because the roots of a quadratic equation with irrational numbers always occur in conjugate pairs.

Solution:
The quadratic equation with roots α and β is given by:

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

Let the roots be $$3 + \sqrt{5}$$​ and $$3 - \sqrt{5}.$$​​

Sum of roots =$$3 + \sqrt{5} + 3 - \sqrt{5} = 6$$​​

Product of the roots = $$(3 + \sqrt{5})(3 - \sqrt{5}) = 3^2 - (\sqrt{5})^2 = 9 - 5 = 4$$​

The quadratic equation is:

​$$x^2 - (\text{Sum of the roots})x + \text{Product of the roots} = 0$$​​

​$$x^2 - 6x + 4 = 0$$​