Multiple choice

Find the value of $k$ so that the sum of the roots of the quadratic equation $\displaystyle { kx }^{ 2 }+2x+3k=0$ is equal to their product.

  1. $\displaystyle \frac { 2 }{ 3 } $
  2. $\displaystyle \frac { -2 }{ 3 } $
  3. $\displaystyle \frac { 3 }{ 2 } $
  4. $\displaystyle \frac { -3 }{ 2 } $
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B Correct answer
Explanation

For kx^2 + 2x + 3k = 0, sum of roots = -2/k, product of roots = 3k/k = 3. Setting sum = product: -2/k = 3, so k = -2/3.

AI explanation

For the quadratic equation kx^2 + 2x + 3k = 0, the sum of the roots is -2/k and the product of the roots is 3k/k which simplifies to 3. Setting the sum equal to the product gives the equation -2/k = 3. Solving for k, we find k = -2/3.

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