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2023 Thailand Online MO
2
2
Part of
2023 Thailand Online MO
Problems
(1)
not all roots of x^3P(x)+1 are real
Source: 2023 Thailand Online MO P2
2/12/2023
Let
P
(
x
)
P(x)
P
(
x
)
be a polynomial with real coefficients. Prove that not all roots of
x
3
P
(
x
)
+
1
x^3P(x)+1
x
3
P
(
x
)
+
1
are real.
algebra
polynomial
polynomial roots