MOD Intermediate

Problem - 2634
Solve $4x^2+27x-9\equiv 0\pmod{15}$

This equation has no solution. The modulo $15$ has two prime divisors: $3$ and $5$. Among all residues of $15$, only $f(3)\equiv 0 \pmod{3}$, but $ f(3)\equiv -7 \not\equiv 0 \pmod{5}$. Therefore, it cannot hold simultaneously which means the original equation does not have any solution.

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