2.6 Let f(x) = x² + ax+bZ[x] be a quadratic polynomial with integer coefficients, for example, f(x) = x²+x+6. Formulate a conjecture about when the set {f(n): ne Z and f(n) is prime} is infinite. Give numerical evidence that supports your conjecture.

2.6 Let f(x) = x² + ax+bZ[x] be a quadratic polynomial with integer coefficients, for example, f(x) = x²+x+6. Formulate a conjecture about when the set {f(n): ne Z and f(n) is prime} is infinite. Give numerical evidence that supports your conjecture.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.CR: Chapter Review

Problem 61E

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Question

2.6 Let f(x) = x² + ax+b € Z[x] be a quadratic polynomial with integer
coefficients, for example, f(x) = x² + x + 6. Formulate a conjecture
about when the set
{f(n): ne Z and f(n) is prime}
is infinite. Give numerical evidence that supports your conjecture.

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