Multiple choice

Find the roots of equation: $\displaystyle { x }^{ 2 }-\frac { 1 }{ 12 } x-\frac { 1 }{ 12 } =0$

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

Multiply by 12: 12x^2 - x - 1 = 0. Factor: (4x + 1)(3x - 1) = 0. Roots are -1/4 and 1/3.

AI explanation

Multiply the entire equation by 12 to clear the fraction, resulting in 12x^2 - x - 1 = 0. Factor this quadratic equation by splitting the middle term to get 12x^2 - 4x + 3x - 1 = 0. This factors into 4x(3x - 1) + 1(3x - 1) = 0, or (4x + 1)(3x - 1) = 0. Setting each factor to zero gives x = -1/4 and x = 1/3.

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