Track / Stage 4 / 214 of 340 #474 of 1964

Problem 474

AMC 12 late, AIME early

Algebra Difficulty 4.8 Find the answer

Determine how many different values of $a$ exist for which the equation

$\left(a^{2}-5\right) x^{2}-2 a x+1=0$

has a unique solution

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Answer: 2. (C)

Options.

$\begin{array}{|l|l|l|l|l|l|l|l|l|} \hline \mathbf{A} & 0 & \mathbf{B} & 1 & \mathbf{C} & 2 & \mathbf{D} & 3 & \mathbf{E} \\ \hline \end{array}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.