Multiple choice

Solve the following quadratic equation by factorization, the roots are : $9x^2$ - 3x - 2 = 0

  1. $\dfrac{2}{3}, \, -\dfrac{1}{6}$
  2. $\dfrac{2}{5}, \, -\dfrac{1}{3}$
  3. $\dfrac{1}{3}, \, -\dfrac{1}{3}$
  4. $\dfrac{2}{3}, \, -\dfrac{1}{3}$
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D Correct answer
Explanation

9x^2 - 3x - 2 = 0. Using quadratic formula: x = [3 +/- sqrt(9 - 4*9*-2)] / 18 = [3 +/- sqrt(9 + 72)] / 18 = [3 +/- 9] / 18. Roots are 12/18 = 2/3 and -6/18 = -1/3.

AI explanation

To solve 9x^2 - 3x - 2 = 0, we split the middle term to get 9x^2 - 6x + 3x - 2 = 0. Factoring by grouping gives 3x(3x - 2) + 1(3x - 2) = 0, which becomes (3x + 1)(3x - 2) = 0. Setting each factor to zero yields the roots 2/3 and -1/3.

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