Multiple choice

If the equation 4x2 - 2kx + 3k = 0 has equal roots, then what are the values of k?

  1. 4, 12

  2. 4, 8

  3. 0, 12

  4. 0, 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For equal roots, the discriminant D = b^2 - 4ac = 0. Here, (-2k)^2 - 4(4)(3k) = 0, so 4k^2 - 48k = 0. Factoring gives 4k(k - 12) = 0, so k = 0 or k = 12.

AI explanation

Using the condition for equal roots in a quadratic equation, the discriminant b squared minus 4ac must equal zero. Substituting the values from 4x2 - 2kx + 3k = 0 gives the equation (-2k) squared minus 4 times 4 times 3k = 0. This simplifies to 4k squared minus 48k = 0, and dividing by 4 gives k squared minus 12k = 0. Factoring out k results in k(k - 12) = 0, meaning the values of k are 0 and 12.

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