Multiple choice

The roots of the equation $3x^{2} - 4x + 3 = 0$ are :

  1. real and unequal

  2. real and equal

  3. imaginary

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The discriminant of the quadratic equation ax^2 + bx + c = 0 is D = b^2 - 4ac. For 3x^2 - 4x + 3 = 0, D = (-4)^2 - 4(3)(3) = 16 - 36 = -20. Since the discriminant is negative, the roots are imaginary.

AI explanation

To determine the nature of the roots of 3x^2 - 4x + 3 = 0, calculate the discriminant using the formula D = b^2 - 4ac. Substituting the values gives D = (-4)^2 - 4(3)(3) = 16 - 36 = -20. Because the discriminant is less than zero, the roots are imaginary.

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