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HMMT 2007 A6

  • Algebra
  • Answer

Consider the polynomial P(x)=x3+x2−x+2P(x)=x^{3}+x^{2}-x+2. Determine all real numbers rr for which there exists a complex number zz not in the reals such that P(z)=rP(z)=r.

Dataset text NuminaMath olympiads. Quoted with source.

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r>\mathbf{3}, \mathbf{r}<\frac{\mathbf{4 9}}{\mathbf{2 7}}

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