The roots of the quadratic equation 2x2 -2√2x + 1 = 0 are ………�

1.	The roots of the quadratic equation 2x2 -2√2x + 1 = 0 are ……………A) √2, 1/√2B) 1/2, 1/2C) 1/√2, 1/√2D) √2,√2
Answer» Correct option is (C) 1/√2, 1/√2 Given quadratic equation is \(2x^2-2\sqrt{2}x+1=0\) \(\Rightarrow2x^2-\sqrt{2}x-\sqrt{2}x+1=0\) \(\Rightarrow\sqrt{2}x(\sqrt{2}x-1)-1(\sqrt{2}x-1)=0\) \(\Rightarrow(\sqrt{2}x-1)(\sqrt{2}x-1)=0\) \(\Rightarrow\sqrt{2}x-1=0\) \(or\;\sqrt{2}x-1=0\) \(\Rightarrow\) \(x=\frac1{\sqrt2}\) or \(x=\frac1{\sqrt2}\) Hence, the roots of given quadratic equation are \(\frac{1}{\sqrt{2}}\;and\;\frac{1}{\sqrt{2}}.\) Correct option is C) 1/√2 , 1/√2

The roots of the quadratic equation 2x2 -2√2x + 1 = 0 are ……………A) √2, 1/√2B) 1/2, 1/2C) 1/√2, 1/√2D) √2,√2

Answer»

Correct option is (C) 1/√2, 1/√2

Given quadratic equation is

\(2x^2-2\sqrt{2}x+1=0\)

\(\Rightarrow2x^2-\sqrt{2}x-\sqrt{2}x+1=0\)

\(\Rightarrow\sqrt{2}x(\sqrt{2}x-1)-1(\sqrt{2}x-1)=0\)

\(\Rightarrow(\sqrt{2}x-1)(\sqrt{2}x-1)=0\)

\(\Rightarrow\sqrt{2}x-1=0\) \(or\;\sqrt{2}x-1=0\)

\(\Rightarrow\) \(x=\frac1{\sqrt2}\) or \(x=\frac1{\sqrt2}\)

Hence, the roots of given quadratic equation are \(\frac{1}{\sqrt{2}}\;and\;\frac{1}{\sqrt{2}}.\)

Correct option is C) 1/√2 , 1/√2