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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations

For the quadratic equation 3x² − 12x + k = 0 to have two equal real roots, what must be the value of k?

The value of k is 12. Equal real roots require the discriminant to be zero. Here b² − 4ac = 144 − 4(3)(k) = 144 − 12k, and setting this equal to zero gives k = 12.

  1. A12Correct
  2. B16
  3. C4
  4. D−12

Explanation

Equal roots need discriminant zero: b² − 4ac = 144 − 12k = 0, so k = 12. The value 16 would come from wrongly using b²/4a... (144/9), which is an incorrect formula.

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