Multiple choice

Values of k for which the quadratic equation $2x^2-kx+k=0$ has equal roots is?

  1. $0$ only
  2. $4$
  3. $8$ only
  4. $0, 8$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. Here, (-k)^2 - 4(2)(k) = 0. k^2 - 8k = 0. k(k - 8) = 0. So k = 0 or k = 8.

AI explanation

For a quadratic equation ax^2 + bx + c = 0 to have equal roots, its discriminant (b^2 - 4ac) must equal zero. Substituting a = 2, b = -k, and c = k gives the equation (-k)^2 - 4(2)(k) = 0, which simplifies to k^2 - 8k = 0. Factoring this as k(k - 8) = 0 yields the values k = 0 and k = 8.

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