1963 AHSME Problems/Problem 28
Problem
Given the equation with real roots. The value of for which the product of the roots of the equation is a maximum is:
Solution
By Vieta's Formulas, the product of the roots is . This value increases as increases.
Also, the quadratic’s roots are real, then the discriminant is greater than or equal to zero, so
Thus, the value that maximizes the product of the roots is , which is answer choice .
See Also
1963 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
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 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.