Question

The roots of the equation $x^2-2\sqrt{2}x+1=0$ are-

• A. Real and distinct
• B. Imaginary and different
• C. Real and equal
• D. Rational and different.

Answer 1

The correct option is A Real and distinct

Nature of the roots of a quadratic equation $a{x}^2+bx+c=0$ depends upon the value of discriminant $D=b^2-4ac$

Given equation is $x^2-2\sqrt{2}x+1=0$

$\therefore D={\left(2\sqrt{2}\right)}^2-4\times 1\times 1=8-4=4$

$⟹D=4>0$

Roots of the given quadratic equation are real and distinct ($\because D>0$ )