Six Zeros of a Hybrid

★ 7/10functions Quadratic Equations trigonometry Casework

Problem

Let $a \in \mathbb{R}$ and

f(x) = \begin{cases} \cos(2\pi x - 2\pi a), & x < a, \\ x^2 - 2(a+1)x + a^2 + 5, & x \geqslant a. \end{cases}

If $f(x)$ has exactly $6$ zeros in $(0, +\infty)$ , find the range of possible values of $a$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Quadratic Equations, trigonometry, Casework

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