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

A firm's break-even condition is modelled by x² − 8x + 15 = 0, where x is output in hundreds of units. Without solving, the sum and product of the roots are respectively:

Sum of roots equals −b/a, which is 8, and product equals c/a, which is 15. The discriminant 64 − 60 = 4 is positive, so the roots are real, namely 3 and 5, which add to 8 and multiply to 15.

  1. A8 and 15Correct
  2. B−8 and 15
  3. C8 and −15
  4. D15 and 8

Explanation

For ax² + bx + c = 0, sum = −b/a = 8 and product = c/a = 15. D = 64 − 60 = 4 > 0, so the roots are real (3 and 5), consistent with sum 8 and product 15. Option 2 forgets the negative sign in −b/a.

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