Multiple choice

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

  1. Real and distinct

  2. Imaginary and different

  3. Real and equal

  4. Rational and different.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The discriminant D = b^2 - 4ac = (-2*sqrt(2))^2 - 4(1)(1) = 8 - 4 = 4. Since D > 0 and is a perfect square, the roots are real, distinct, and rational.

AI explanation

To find the nature of the roots, compute the discriminant, which is b squared minus 4ac, using the values 2 times the square root of 2 for b, negative 1 for a, and 1 for c. This gives the discriminant as 8 minus 4 times 1 times 1, which equals 4. Since the discriminant is greater than zero and not a perfect square, the roots are real and distinct.

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