Multiple choice

Find the roots of the quadratic equation $3x^2 - 5x -12 = 0$ by using the quadratic formula.

  1. $-\cfrac{2}{3},3$
  2. $-\cfrac{4}{3},-3$
  3. $-\cfrac{-4}{3},-3$
  4. $-\cfrac{4}{3},3$
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D Correct answer
Explanation

For 3x^2 - 5x - 12 = 0, a=3, b=-5, c=-12. Discriminant = (-5)^2 - 4(3)(-12) = 25 + 144 = 169. Roots = (5 +/- 13) / 6. Roots are 18/6 = 3 and -8/6 = -4/3.

AI explanation

Using the quadratic formula, we evaluate x = (5 + sqrt(25 - 4(3)(-12))) / 6 = (5 + 13) / 6 = 3 for the positive root. Evaluating for the negative root gives x = (5 - sqrt(169)) / 6 = (5 - 13) / 6 = -4/3. The roots are 3 and -4/3.

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