query: Suppose $P(x)$ is a polynomial with $P(2)=2017$ and $P(5)=2002$. If it is given that $P(x)=0$ has exactly one integer root, find that root.
positive_passages.docid: 157487
positive_passages.text: Showing a polynomial having at least one integer root under certain conditions has precisely one integer root
negative_passages.docid: 95594
negative_passages.text: Prove that a polynomial is irreducible or the field contains a $p$th root
negative_passages.docid: 111569
negative_passages.text: Property of a polynomial with no positive real roots
negative_passages.docid: 103246
negative_passages.text: Prove that a polynomial of degree $d$ has at most $d$ roots (without induction)
negative_passages.docid: 141184
negative_passages.text: Proof that a degree 4 polynomial has at least two roots
negative_passages.docid: 51019
negative_passages.text: Polynomial problem with two conditions
negative_passages.docid: 66960
negative_passages.text: Find a polynomial f(x) of degree 5 such that 2 properties hold.
negative_passages.docid: 134342
negative_passages.text: Find a polynomial of degree > 0 in $\mathbb Z_4[X]$ that is a unit.
negative_passages.docid: 113386
negative_passages.text: Find all integer roots of: $x^2(y-1)+y^2(x-1)=1$
negative_passages.docid: 133101
negative_passages.text: Number of solutions of $P(x)=e^{ax}$ if $P$ is a polynomial
negative_passages.docid: 143466
negative_passages.text: Roots of functions / polynomials
negative_passages.docid: 109102
negative_passages.text: Determine all real polynomials with $P(0)=0$ and $P(x^2+1)=(P(x))^2+1$
negative_passages.docid: 49899
negative_passages.text: Determine the number of real roots
negative_passages.docid: 56068
negative_passages.text: What actually is a polynomial?
negative_passages.docid: 105679
negative_passages.text: Can $\pi$ or $e$ be a root of a polynomial with algebraic coefficients?
negative_passages.docid: 3036
negative_passages.text: Is a polynomial equation of degree $\ge 5$ not solvable by any way?
negative_passages.docid: 127524
negative_passages.text: how to find the remainder when a polynomial $p(x)$ is divided my another polynomial $q(x)$