1981 AMC 12 Problem 30
Attempt Problem 30 of the 1981 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 1981 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 are the solutions of the equation then an equation whose solutions are is
none of these
Answer: D
Small hint:
Use the missing cubic term to find
Big hint:
Each listed expression becomes the negative reciprocal of one original root
Solution:
Vieta’s formulas give Thus, for example, and similarly the new roots are Put in Multiplying by gives or
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
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- 1961 AMC 12
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- 1963 AMC 12
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