Multiple choice

Find $k$, if the sum of the roots of the quadratic equation $4x^2\,+\,8kx\,+\,k\,+\,9\,=\,0$ is equal to their product.

  1. $1$
  2. $3$
  3. $-1$
  4. $-3$
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C Correct answer
Explanation

Sum of roots = -8k/4 = -2k. Product of roots = (k+9)/4. -2k = (k+9)/4. -8k = k + 9. -9k = 9, k = -1.

AI explanation

For the quadratic equation 4x^2 + 8kx + k + 9 = 0, the sum of the roots is -8k/4 = -2k and the product is (k + 9)/4. Equating the sum and product yields -2k = (k + 9)/4. Multiplying by 4 gives -8k = k + 9, meaning -9k = 9, so k = -1.

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