CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
A firm's break-even output x (in units) satisfies x² − 70x + 1000 = 0. What is the product of the two break-even outputs, and what is their sum?
The product of the break-even outputs is 1000 and their sum is 70. The sum of roots is −b/a = 70 and the product is c/a = 1000. The roots 20 and 50 confirm this, so the other combinations are incorrect.
- AProduct 70, sum 1000
- BProduct 1000, sum 70Correct
- CProduct 1000, sum −70
- DProduct −1000, sum 70
Explanation
For x² − 70x + 1000 = 0, the sum of roots is −(−70)/1 = 70 and the product is 1000/1 = 1000. Check: the roots are 20 and 50, which sum to 70 and multiply to 1000. Swapping the two values or the sign of the sum gives the other options, all wrong.
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