Two Zeros of a Clamp

Problem

Let

f(x) = \begin{cases} -1, & x \leqslant -1,\\ x, & -1 < x < 1,\\ 1, & x \geqslant 1, \end{cases} \qquad g(x) = ax^2 - x + 1.

If $y = f(x) - g(x)$ has exactly $2$ distinct zeros, find the range of possible values of the real number $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Substitution, Casework

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