Multiple choice

The value of k for which the quadratic equation $x^2-2kx+5k=0$ has equal roots,are

  1. $0$ only
  2. $5$ only
  3. $0$, $5$
  4. $0$, $6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac must be 0. Here, (-2k)^2 - 4(1)(5k) = 4k^2 - 20k = 0. Factoring gives 4k(k - 5) = 0, so k = 0 or k = 5.

AI explanation

For the quadratic equation x^2 - 2kx + 5k = 0 to have equal roots, the discriminant must equal zero, so b^2 - 4ac = 0. Substituting the values gives (-2k)^2 - 4(1)(5k) = 0, which simplifies to 4k^2 - 20k = 0. Factoring out 4k leaves 4k(k - 5) = 0, which means k = 0 or k = 5.

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