Multiple choice

Determine the nature of roots of the equation $x^2 + 2x\sqrt{3}+3=0$.

  1. Real and distinct

  2. Non-real and distinct

  3. Real and equal

  4. Non-real and equal
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The discriminant of the quadratic equation x^2 + 2x*sqrt(3) + 3 = 0 is D = b^2 - 4ac. Here, a=1, b=2*sqrt(3), and c=3. D = (2*sqrt(3))^2 - 4(1)(3) = 12 - 12 = 0. Since the discriminant is zero, the roots are real and equal.

AI explanation

To find the nature of the roots of x^2 + 2x times the square root of 3 + 3 = 0, calculate the discriminant using the formula D = b^2 - 4ac. Substituting the values gives D = (2 times the square root of 3)^2 - 4(1)(3) = 12 - 12 = 0. Since the discriminant is equal to zero, the roots are real and equal.

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