The integral values of $a$ for which the equation $cos^2x-(a^2+a+5)|cosx|+(a^3+3a^2+2a+6)$ has real solutions. This question is from a math quiz so the answer cannot be that long..
2026-04-04 16:12:11.1775319131
Finding the integral values
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Hint
Expression is equivalent to $$ (|\cos x| - (a^2 + 2))(|\cos x| - (a + 3))=0 $$
Only solution comes from when $|\cos x| = a + 3$. So $$ -1 \leq a+3 \leq 1 $$