Multiple choice

The discrimination of the equation $x^2 + 2x\sqrt3 + 3 = 0$ is zero. Hence, its roots are:

  1. Real and Equal

  2. Rational and Equal

  3. Rational and Unequal

  4. Irrational and Unequal

  5. Imaginary
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A Correct answer
Explanation

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

AI explanation

For any quadratic equation, if the discriminant is exactly zero, the roots are always real and equal. This property holds true regardless of the specific numbers involved, as zero discriminant indicates the curve touches the x-axis at exactly one point. Therefore, the roots of the given equation are real and equal.

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