Multiple choice

If the sum of the roots of the equation $3x^2 + (2k+1)x-5=0$ is equal to the product of the roots, then $k$ equals

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

Sum of roots = -(2k+1)/3. Product of roots = -5/3. Equating them: -(2k+1)/3 = -5/3 => 2k+1 = 5 => 2k = 4 => k = 2.

AI explanation

For the quadratic equation 3x^2 + (2k + 1)x - 5 = 0, the sum of the roots is -(2k + 1)/3 and the product of the roots is -5/3. Equating the sum and the product gives -(2k + 1)/3 = -5/3. Multiplying both sides by -3 results in 2k + 1 = 5. Solving for k, we subtract 1 to get 2k = 4, which means k equals 2.

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