If one of the roots of a quadratic equation with rational coefficients is 2 +√3 then the qnadmtic equation is given as_________.

Correct option is B

​Given:
One root = $$2 + \sqrt{3}$$​​

Solution:

Use the fact that for a quadratic equation with roots $$r_1$$​ and $$r_2$$​ , the equation can be written as:

​$$(x - r_1)(x - r_2) = 0$$​​

Here, $$r_1 = 2 + \sqrt{3}$$​ and $$r_2 = 2 - \sqrt{3}$$​

Multiply the factors:

$$(x - (2 + \sqrt{3}))(x - (2 - \sqrt{3})) = 0$$ 

​$$(x - 2 - \sqrt{3})(x - 2 + \sqrt{3}) = 0 \\ \ \\ (x - 2)^2 - (\sqrt{3})^2= 0 \\ \ \\ (x - 2)^2 - 3 = 0$$​​ ​

​$$x^2 - 4x + 4 - 3 =0 \\ \ \\ x^2 - 4x +1 = 0$$​​