Multiple choice

Solve the following quadratic equation by factorization method: $3x^2-5x-12=0$

  1. $\left \{ -\dfrac{4}{3}, 3 \right \}$ 
  2. $\left \{ \dfrac{4}{3}, 3 \right \}$ 
  3. $\left \{ -\dfrac{4}{3}, -3 \right \}$ 

  4. None of these
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A Correct answer
Explanation

3x^2 - 5x - 12 = 0 -> 3x^2 - 9x + 4x - 12 = 0 -> 3x(x - 3) + 4(x - 3) = 0 -> (3x + 4)(x - 3) = 0. Roots are -4/3 and 3.

AI explanation

To solve 3x^2 - 5x - 12 = 0 by factorization, we find two numbers that multiply to (3 * -12) = -36 and add to -5, which are -9 and 4. We rewrite the middle term to form 3x^2 - 9x + 4x - 12 = 0. Factoring by grouping yields 3x(x - 3) + 4(x - 3) = 0, giving the factors (3x + 4)(x - 3) = 0. Setting each factor to zero results in the solution set {-4/3, 3}.

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