Multiple choice

Solve the following quadratic equation by factorization, the roots are : $3x^2$ $+11x + 10$

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

Factor 3x^2 + 11x + 10 = 3x^2 + 6x + 5x + 10 = 3x(x + 2) + 5(x + 2) = (3x + 5)(x + 2). Setting each factor to zero gives x = -5/3 and x = -2.

AI explanation

For the equation 3x^2 + 11x + 10 = 0, we split the middle term to rewrite it as 3x^2 + 6x + 5x + 10 = 0. Factoring by grouping gives 3x(x + 2) + 5(x + 2) = 0, which simplifies to (3x + 5)(x + 2) = 0. Equating each factor to zero gives the roots -5/3 and -2.

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