Multiple choice

The sum of the roots and the product of roots of a quadratic equation $3x^2-(2K+1)x-K-5=0$ are equal. The value of $K$ will be

  1. $-\displaystyle\frac{1}{2}$
  2. $-2$
  3. $\displaystyle\frac{1}{2}$
  4. $5$
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B Correct answer
Explanation

Sum of roots = (2K+1)/3 and product of roots = (-K-5)/3. Setting them equal: 2K + 1 = -K - 5. Solving for K gives 3K = -6, so K = -2.

AI explanation

For a quadratic equation ax^2 + bx + c = 0, the sum of the roots is -b/a and the product is c/a. Setting the sum equal to the product gives (2K + 1)/3 = (-K - 5)/3. Solving this linear equation, 2K + 1 = -K - 5, results in 3K = -6 and K = -2.

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