Multiple choice

Find the roots of the following quadratic equations by the method of completing the squares $2 \sqrt 2 x^2 + \sqrt {15}x + \sqrt 2 = 0$

  1. No real solution
  2. $x=\sqrt{\dfrac{2}{3}}\pm \dfrac{41}{\sqrt{3}}i$

  3. Cannot be determined

  4. None of these
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A Correct answer
Explanation

The discriminant D = b^2 - 4ac = (sqrt(15))^2 - 4(2*sqrt(2))(sqrt(2)) = 15 - 4(4) = 15 - 16 = -1. Since D < 0, there are no real solutions.

AI explanation

To determine the nature of the roots, we calculate the discriminant of the quadratic equation using the formula D = b^2 - 4ac. Substituting the values gives D = (sqrt(15))^2 - 4*(2*sqrt(2))*(sqrt(2)), which simplifies to 15 - 16 = -1. Because the discriminant is negative, the quadratic equation has no real roots. The result is no real solution.

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