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

For the equation x² − 6x + c = 0, the roots are real and distinct only for certain integer values of c. How many positive integer values of c make the roots real and distinct?

There are 8 such values. The discriminant is 36 − 4c, which must be positive for real and distinct roots, so c < 9. The positive integers 1 through 8 qualify; c = 9 gives equal roots and is excluded.

  1. A8Correct
  2. B9
  3. C10
  4. D5

Explanation

Distinct real roots need 36 − 4c > 0, so c < 9. Positive integers satisfying this are 1 to 8, which is 8 values. Option B counts c = 9, which gives D = 0 (equal roots), so it is wrong.

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