1953 AHSME Problems/Problem 44
Problem
In solving a problem that reduces to a quadratic equation one student makes a mistake only in the constant term of the equation and obtains and for the roots. Another student makes a mistake only in the coefficient of the first degree term and find and for the roots. The correct equation was:
Solution
Let represent the correct equation. Since the coefficient of the term is , the sum of the roots is , and the product of the roots is .
If a student only misreads the constant term, he must have the correct sum of roots. Therefore, the sum of the roots is , so . If a student only misreads the linear term, he must have the correct product of the roots. The product of the roots is , so . The correct equation is .
See Also
1953 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 43 |
Followed by Problem 45 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.