Multiple choice

The solution set for the quadratic equation 6x2 - x - 2 = 0 is

  1. {2/3, -1/2}

  2. {2/3, 1/2}

  3. {-2/3, -1/2}

  4. None of these
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A Correct answer
Explanation

6x^2 - x - 2 = 0. Using the quadratic formula or factoring: 6x^2 - 4x + 3x - 2 = 0 => 2x(3x - 2) + 1(3x - 2) = 0 => (2x + 1)(3x - 2) = 0. The roots are x = -1/2 and x = 2/3.

AI explanation

To find the solution set for 6x^2 - x - 2 = 0, we factor the quadratic equation by splitting the middle term. We look for two numbers that multiply to (6)(-2) = -12 and add to -1, which are -4 and 3. Rewriting the middle term gives 6x^2 - 4x + 3x - 2 = 0, which factors into 2x(3x - 2) + 1(3x - 2) = 0. Setting (2x + 1)(3x - 2) = 0 gives the roots x = -1/2 and x = 2/3.

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