Multiple choice

For which set of values of k, the equation x2 - kx + 36 = 0 has equal roots?

  1. k = 12, k = 13

  2. k = 12, k = 0

  3. k = 11, k = 13

  4. k = 12, k = - 12
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(1)(36) = 0. k^2 = 144, so k = 12 or -12.

AI explanation

A quadratic equation of the form ax^2 + bx + c = 0 has equal roots when its discriminant, given by b^2 - 4ac, equals zero. For the equation x^2 - kx + 36 = 0, we set the discriminant to zero: (-k)^2 - 4(1)(36) = 0. This simplifies to k^2 - 144 = 0, which can be factored as (k - 12)(k + 12) = 0. Solving this gives the values k = 12 and k = -12.

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