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

A firm's break-even condition leads to the equation 2x² − 8x + 9 = 0. What does the discriminant indicate about the break-even output x?

No real break-even output exists. The discriminant is (−8)² − 4(2)(9) = 64 − 72 = −8, which is negative, so the quadratic has no real roots and the output level cannot satisfy the equation.

  1. ANo real value of x exists, since the discriminant is −8Correct
  2. BTwo equal real values exist, since the discriminant is 0
  3. CTwo distinct real values exist, since the discriminant is 8
  4. DTwo distinct real values exist, since the discriminant is 136

Explanation

D = (−8)² − 4(2)(9) = 64 − 72 = −8, which is negative, so the roots are not real. Hence no real break-even output exists. Option D wrongly adds 4ac instead of subtracting it: 64 + 72 = 136.

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