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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_14 / For how many ordered pairs (a,b) of integers does the polynomial x³+ax²+bx+6 have 3 distinct integer roots?

Problem

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problem

For how many ordered pairs

(a,b)

of integers does the polynomial

x^3+ax^2+bx+6

have

3

distinct integer roots?

Plain-text mathematical notation (without MathML)

For how many ordered pairs (a,b) of integers does the polynomial x³+ax²+bx+6 have 3 distinct integer roots?

Original LaTeX notation

For how many ordered pairs $(a,b)$ of integers does the polynomial $x^3+ax^2+bx+6$ have $3$ distinct integer roots?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_14
task_id: 53e0f6c7-8986-5935-8882-94bb6772c357
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f14
task_revision_id: 2
config / split: default / train

Official source

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