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Omni-MATH / Let P(x)=x³+ax²+bx+2015 be a polynomial all of whose roots are integers. Given that P(x)≥0 for all x≥0, find the sum of all possible values of P(−1).

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problem

Let P(x)=x3+ax2+bx+2015P(x)=x^{3}+a x^{2}+b x+2015 be a polynomial all of whose roots are integers. Given that P(x)≥0P(x) \geq 0 for all x≥0x \geq 0, find the sum of all possible values of P(−1)P(-1).
Plain-text mathematical notation (without MathML)
Let P(x)=x³+ax²+bx+2015 be a polynomial all of whose roots are integers. Given that P(x)≥0 for all x≥0, find the sum of all possible values of P(−1).
Original LaTeX notation
Let $P(x)=x^{3}+a x^{2}+b x+2015$ be a polynomial all of whose roots are integers. Given that $P(x) \geq 0$ for all $x \geq 0$, find the sum of all possible values of $P(-1)$.

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Source and history

task_id
b20d56d7-3a68-56e2-8f13-03182815e455
task_key
test--b20d56d7-3a68-56e2-8f13-03182815e455
task_revision_id
1
config / split
/ test

Official source

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