Multiple choice

Determine the nature of roots of the following equations from the discriminant: $2x^2\,+\,5\sqrt{3}x\,+\,16\,=\,0$

  1. real and equal

  2. real and unequal

  3. non real

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Discriminant D = b^2 - 4ac = (5*sqrt(3))^2 - 4(2)(16) = (25*3) - 128 = 75 - 128 = -53. Since D < 0, the roots are non-real.

AI explanation

The nature of the roots is determined by the discriminant formula D = b^2 - 4ac. Here a = 2, b = 5 times square root of 3, and c = 16, so D = 75 - 128 = -53. Since the discriminant is negative, the roots are non real.

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