Multiple choice

Find the discriminant for the given quadratic equation: $\sqrt{3}x^2\,+\,2\sqrt{2}x\,-\,2\sqrt{3}\,=\,0$

  1. $26$
  2. $32$
  3. $38$
  4. $44$
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B Correct answer
Explanation

Discriminant D = b^2 - 4ac. Here a = sqrt(3), b = 2*sqrt(2), c = -2*sqrt(3). D = (2*sqrt(2))^2 - 4 * sqrt(3) * (-2*sqrt(3)) = 8 - 4 * (-6) = 8 + 24 = 32.

AI explanation

The discriminant of a quadratic equation ax^2 + bx + c = 0 is calculated as D = b^2 - 4ac. For the given equation, the coefficients are a = square root of 3, b = 2 times the square root of 2, and c = -2 times the square root of 3. Substituting these values gives D = (2 times the square root of 2)^2 - 4(square root of 3)(-2 times the square root of 3), which simplifies to 8 + 24, resulting in a discriminant of 32.

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