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MATH / Suppose the polynomial

Problem

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problem

Suppose the polynomial f(x)=anxn+an−1xn−1+⋯+a2x2+a1x+a0f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_2x^2 + a_1x + a_0has integer coefficients, and its roots are distinct integers. Given that an=2a_n=2 and a0=66a_0=66, what is the least possible value of |an−1||a_{n-1}|?
Plain-text mathematical notation (without MathML)
Suppose the polynomial
f(x)=a_(n)x^(n)+a_(n−1)x^(n−1)+⋯+a₂x²+a₁x+a₀has integer coefficients, and its roots are distinct integers.

Given that a_(n)=2 and a₀=66, what is the least possible value of |a_(n−1)|?
Original LaTeX notation
Suppose the polynomial
$$f(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_2x^2 + a_1x + a_0$$has integer coefficients, and its roots are distinct integers.

Given that $a_n=2$ and $a_0=66$, what is the least possible value of $|a_{n-1}|$?

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
0d424094-786a-523f-b0d3-688210396301
task_key
intermediate~5falgebra--test--0d424094-786a-523f-b0d3-688210396301
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import