1964 AMC 12 Problem 30
Attempt Problem 30 of the 1964 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 1964 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
30.
If
the larger root minus the smaller root is:
Answer: D
Small hint:
Notice that
Big hint:
For the root difference is
Solution:
Let and The discriminant is Hence the root difference is
Therefore, the correct answer is D.
Problem 30 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
- 1963 AMC 12
- 1965 AMC 12
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- 1967 AMC 12
- 1968 AMC 12
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- 1971 AMC 12
- 1972 AMC 12
- 1973 AMC 12
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- 1978 AMC 12
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- 1989 AMC 12
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- 1995 AMC 12
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- 1999 AMC 12