A quadratic equation, whose roots are 2 + √3 and 2 – √3 = ……

1.	A quadratic equation, whose roots are 2 + √3 and 2 – √3 = ………………. A) x2 – x – 4 = 0 B) x2 – 4x + 1 = 0 C) x2 + 4x + 3 = 0 D) x2 + x – 3 = 0
Answer» 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 \((x-(2+\sqrt{3}))(x-(2-\sqrt{3}))=0\) \(\Rightarrow((x-2)-\sqrt3)((x-2)+\sqrt3)=0\) \(\Rightarrow(x-2)^2-(\sqrt3)^2=0\) \((\because(a-b)(a+b)=a^2-b^2)\) \(\Rightarrow x^2-4x+4-3=0\) \((\because(a-b)^2=a^2-2ab+b^2)\) \(\Rightarrow x^2-4x+1=0\) Correct option is B) x² – 4x + 1 = 0

A quadratic equation, whose roots are 2 + √3 and 2 – √3 = ………………. A) x2 – x – 4 = 0 B) x2 – 4x + 1 = 0 C) x2 + 4x + 3 = 0 D) x2 + x – 3 = 0

Answer»

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

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

\(\Rightarrow((x-2)-\sqrt3)((x-2)+\sqrt3)=0\)

\(\Rightarrow(x-2)^2-(\sqrt3)^2=0\) \((\because(a-b)(a+b)=a^2-b^2)\)

\(\Rightarrow x^2-4x+4-3=0\) \((\because(a-b)^2=a^2-2ab+b^2)\)

\(\Rightarrow x^2-4x+1=0\)

Correct option is B) x² – 4x + 1 = 0