Library / Slovenia — National Math Olympiad /4 of 122

Slovenia — National Math Olympiad, 2012

Algebra Difficulty 3.7 AMC 10/12 Find the answer Slovenia

Among the functions below, which takes the value $0$ exactly twice?

Pick one

Solution

The graph of the function given in (A) intersects the $x$ axis infinitely many times, the graph of the function in (B) intersects the $x$ axis in $(\sqrt{3}, 0)$ and $(-\sqrt{3}, 0)$ , the graph of the function in (C) intersects the $x$ axis only in $(0, 0)$ , the graph of the function in (D) intersects the $x$ axis only in $(\frac{1}{2}, 0)$ , and the graph of the function given in (E) intersects the $x$ axis only in $(1, 0)$ . The correct answer is thus (B).

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.