Multiple choice

The roots of the equation 3x2 - 12x + 10 = 0 are

  1. irrational and unequal

  2. rational and equal

  3. rational and unequal

  4. complex
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A Correct answer
Explanation

Discriminant D = b^2 - 4ac = (-12)^2 - 4(3)(10) = 144 - 120 = 24. Since 24 is positive but not a perfect square, the roots are irrational and unequal.

AI explanation

To determine the nature of the roots for 3x^2 - 12x + 10 = 0, we calculate the discriminant using the formula b^2 - 4ac. Substituting the values gives (-12)^2 - 4(3)(10) = 144 - 120 = 24. Since 24 is positive but not a perfect square, the roots are irrational and unequal.

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