Multiple choice

For how many values of k, roots of equation 3x2 − kx +12 = 0 are imaginary?

  1. 23

  2. 0

  3. 2

  4. Infinite values
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For roots to be imaginary, the discriminant D = b^2 - 4ac < 0. Here, (-k)^2 - 4(3)(12) < 0, so k^2 - 144 < 0, meaning k^2 < 144. This holds for any k in the interval (-12, 12). Since there are infinitely many real numbers in this interval, there are infinite values for k.

AI explanation

For the roots of the quadratic equation 3x2 - kx + 12 = 0 to be imaginary, the discriminant must be strictly less than zero, giving (-k)2 - 4(3)(12) < 0. This simplifies to k2 - 144 < 0, meaning k must fall in the range -12 < k < 12. Since k can be any real number in this continuous interval, there are infinitely many values that satisfy the condition.

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