1953 AMC 12 Problem 44
Attempt Problem 44 of the 1953 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 1953 AMC 12 solutions, or check the answer key.
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44.
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 finds and for the roots. The correct equation was:
none of these
Answer: A
Small hint:
The first student’s correct linear coefficient is determined by the sum
Big hint:
The second student’s correct constant term is determined by the product
Solution:
The first student changed only the constant term, so the correct coefficient of is the one in the monic quadratic with roots and it is The second student changed only that linear coefficient, so the correct constant is Therefore the correct equation is
Thus, the correct answer is A.