Question

If one root of the quadratic equation x² – 4x + 1 = 0 is 2 + √3, then the other root is …………

A) 7 + √3 

B) 7 – 4√3 

C) 1 + √3 

D) 2 – √3

Answer 1

Correct option is (D) 2 – √3

Given quadratic equation is \(x^2-4x+1=0\)

Let the other root be x.

\(\therefore\) Sum of roots \(=\frac{-(-4)}1=4\)

\(\Rightarrow\) \(x+2+\sqrt{3}=4\)

\(\Rightarrow\) \(x=4-2-\sqrt3\)

\(\Rightarrow\) x = \(2-\sqrt{3}\)

Hence, the other root is \(2-\sqrt{3}.\)

Answer 2

Correct option is D) 2 – √3