Multiple choice

Solve the following quadratic equations by factorization method: $3x-\dfrac{8}{x}=2$

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

  4. None of these
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A Correct answer
Explanation

Multiply by x: 3x^2 - 8 = 2x, so 3x^2 - 2x - 8 = 0. Factoring: 3x^2 - 6x + 4x - 8 = 0, which is 3x(x-2) + 4(x-2) = 0. The roots are x = 2 and x = -4/3.

AI explanation

Multiplying the equation 3x - 8/x = 2 by x clears the denominator, resulting in the quadratic equation 3x^2 - 2x - 8 = 0. By splitting the middle term, we find the numbers -6 and 4 multiply to -24 and add to -2. The equation becomes 3x^2 - 6x + 4x - 8 = 0, which factors into 3x(x - 2) + 4(x - 2) = 0. The resulting factors are (3x + 4)(x - 2) = 0, giving the roots -4/3 and 2.

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