Multiple choice

Solving the following quadratic equation by factorization, the roots are : $-\dfrac{3}{2}, \, \dfrac{-1}{3}$ $6x^2$ + 11x + 3 = 0

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For 6x^2 + 11x + 3 = 0, the roots are found via the quadratic formula: x = [-11 +/- sqrt(121 - 72)] / 12 = [-11 +/- 7] / 12. Roots are -4/12 = -1/3 and -18/12 = -3/2. These match the provided roots.

AI explanation

To verify the roots for 6x^2 + 11x + 3 = 0, we factor the quadratic by splitting the middle term to get 6x^2 + 9x + 2x + 3 = 0. Factoring by grouping gives 3x(2x + 3) + 1(2x + 3) = 0, which becomes (3x + 1)(2x + 3) = 0. Setting each factor to zero results in x = -1/3 and x = -3/2, making the statement True.

Keep practicing — related questions