Showing a polynomial having at least one integer root under certain conditions has precisely one integer root
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$P(x) = 0$ is a polynomial equation having at least one integer root, where $P(x)$ is a polynomial of degree five and having integer coefficients. If $P(2) = 3$ and $P(10)= 11$ , then prove that the equation $P(x) = 0$ has exactly one integer root. I tried by assuming a fifth degree polynomial but got stuck after that. The question was asked by my friend.
polynomials
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edited 1 hour ago
Eevee Trainer
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asked 2 hours ago
Ramanujam