1963 AMC 12 Problem 28
Attempt Problem 28 of the 1963 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1963 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
28.
Given the equation with real roots. The value of for which the product of the roots of the equation is a maximum is:
Answer: D
Small hint:
The product of the roots is
Big hint:
Use the discriminant condition to find the largest allowed
Solution:
Real roots require so The root product is which increases with It is therefore largest at
Thus, the correct answer is D.
Problem 28 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
- 1953 AMC 12
- 1954 AMC 12
- 1955 AMC 12
- 1956 AMC 12
- 1957 AMC 12
- 1958 AMC 12
- 1959 AMC 12
- 1960 AMC 12
- 1961 AMC 12
- 1962 AMC 12
- 1964 AMC 12
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