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

1.	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» 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 \(2-\sqrt{3}.\) Correct option is D) 2 – √3

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»

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 \(2-\sqrt{3}.\)

Correct option is D) 2 – √3