1956 AMC 12 Problem 42
Attempt Problem 42 of the 1956 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 1956 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
42.
The equation has:
no root
one real root
one real root and one imaginary root
two imaginary roots
two real roots
Answer: A
Small hint:
For real square roots the domain requires
Big hint:
On that domain, compare directly with
Solution:
For a real solution, Then so Consequently and it cannot equal zero. The original equation is a real radical expression, so nonreal roots are outside its domain.
The correct answer is A.