Multiple choice

For what values of $k$, the equation $x^{2}+2(k-4)x+2k=0$ has equal roots?

  1. $8, 2$
  2. $6, 4$
  3. $12, 2$
  4. $10, 4$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For equal roots, the discriminant D = 0. D = [2(k-4)]^2 - 4(1)(2k) = 4(k^2 - 8k + 16) - 8k = 4k^2 - 32k + 64 - 8k = 4k^2 - 40k + 64 = 0. Dividing by 4: k^2 - 10k + 16 = 0. Factors to (k-8)(k-2) = 0. So k = 8 or k = 2.

AI explanation

For a quadratic equation to have equal roots, its discriminant must be zero, so we set D = b^2 - 4ac = 0. Substituting the values gives [2(k - 4)]^2 - 4(1)(2k) = 0, which simplifies to 4(k - 4)^2 - 8k = 0. Dividing by 4 and expanding yields k^2 - 10k + 16 = 0, which factors to (k - 8)(k - 2) = 0, giving the values 8 and 2.

Keep practicing — related questions