Multiple choice

3x² + 5x - 2 = 0 ,What are the roots of the equation?

  1. x = -2, 1/3

  2. x = -5/6, 2/3

  3. x = -5/3, 2/3

  4. x = -5/3, -2/3

  5. None of these
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A Correct answer
Explanation

3x^2 + 5x - 2 = 0. Factoring: 3x^2 + 6x - x - 2 = 0 => 3x(x+2) - 1(x+2) = 0 => (3x-1)(x+2) = 0. Roots are x = 1/3 and x = -2.

AI explanation

To find the roots of 3x^2 + 5x - 2 = 0 using the factoring method, we need two numbers that multiply to (3 times -2) or -6 and add to 5. These numbers are 6 and -1, allowing us to rewrite the middle term as 3x^2 + 6x - x - 2 = 0. Factoring by grouping gives 3x(x + 2) - 1(x + 2) = 0, resulting in (3x - 1)(x + 2) = 0. Setting each factor to zero gives the roots x = 1/3 and x = -2.

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