Correct option is (B) x2 – 4x + 1 = 0
Roots of quadratic equation are \(2+\sqrt{3}\) and \(2-\sqrt{3}.\)
\(\therefore\) Required quadratic equation is
\((x-(2+\sqrt{3}))(x-(2-\sqrt{3}))=0\)
\(\Rightarrow((x-2)-\sqrt3)((x-2)+\sqrt3)=0\)
\(\Rightarrow(x-2)^2-(\sqrt3)^2=0\) \((\because(a-b)(a+b)=a^2-b^2)\)
\(\Rightarrow x^2-4x+4-3=0\) \((\because(a-b)^2=a^2-2ab+b^2)\)
\(\Rightarrow x^2-4x+1=0\)
