Multiple choice

Solve the following quadratic equation by factorization, the roots are : $48x^2$$ -$ $13x - 1 = 0$

  1. $-\dfrac{1}{16}, \, \dfrac{1}{2}$
  2. $-\dfrac{1}{16}, \, \dfrac{1}{4}$
  3. $-\dfrac{1}{6}, \, \dfrac{1}{3}$
  4. $-\dfrac{1}{16}, \, \dfrac{1}{3}$
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D Correct answer
Explanation

Factor 48x^2 - 13x - 1 = 0. We need two numbers that multiply to -48 and add to -13, which are -16 and 3. So, 48x^2 - 16x + 3x - 1 = 0, which factors to 16x(3x - 1) + 1(3x - 1) = 0. The roots are x = 1/3 and x = -1/16.

AI explanation

To solve 48x^2 - 13x - 1 = 0, we split the middle term to get 48x^2 - 16x + 3x - 1 = 0. Factoring by grouping gives 16x(3x - 1) + 1(3x - 1) = 0, which becomes (16x + 1)(3x - 1) = 0. Setting each factor to zero provides the roots -1/16 and 1/3.

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