Multiple choice

Find the roots of the following quadratic equation by using the quadratic formula $2x^2 - 2\sqrt 2x + 1 = 0$

  1. $\displaystyle -\frac{1}{\sqrt 2}, \frac{1}{\sqrt{2}}$
  2. $\displaystyle \frac{1}{\sqrt 2}, \frac{1}{\sqrt{2}}$.
  3. $\displaystyle -\frac{1}{ 2}, \frac{1}{{2}}$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The quadratic formula is x = (-b +/- sqrt(b^2 - 4ac)) / 2a. For 2x^2 - 2*sqrt(2)x + 1 = 0, a=2, b=-2*sqrt(2), and c=1. The discriminant is (2*sqrt(2))^2 - 4(2)(1) = 8 - 8 = 0, so the roots are equal to -b / 2a = (2*sqrt(2)) / 4 = sqrt(2) / 2 = 1 / sqrt(2).

AI explanation

Using the quadratic formula with a equal to 2, b equal to negative 2 times the square root of 2 and c equal to 1, the discriminant is 8 minus 8, which is 0. The root is 2 times the square root of 2, divided by 4, which simplifies to 1 divided by the square root of 2. Since the discriminant is zero, the two equal real roots are both 1 divided by the square root of 2.

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