Multiple choice

Find the sum of the roots for the equation $\dfrac{2}{3}x^{2}-3x + 6 = 0$.

  1. $\dfrac{2}{9}$
  2. $\dfrac{9}{2}$
  3. $\dfrac{2}{6}$
  4. $\dfrac{7}{2}$
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B Correct answer
Explanation

For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a. Here, a = 2/3 and b = -3. Sum = -(-3) / (2/3) = 3 * (3/2) = 9/2.

AI explanation

The sum of the roots of a quadratic equation in the form ax^2 + bx + c = 0 is given by the formula -b/a. In the equation (2/3)x^2 - 3x + 6 = 0, the coefficients are a = 2/3 and b = -3. Substituting these values into the formula gives -(-3) / (2/3), which simplifies to 9/2. The sum of the roots is 9/2.

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