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6
2022 Team 6
2022 Team 6
Source:
March 14, 2022
algebra
complex numbers
polynomial
Problem Statement
Let
P
(
x
)
=
x
4
+
a
x
3
+
b
x
2
+
x
P(x) = x^4 + ax^3 + bx^2 + x
P
(
x
)
=
x
4
+
a
x
3
+
b
x
2
+
x
be a polynomial with four distinct roots that lie on a circle in the complex plane. Prove that
a
b
≠
9
ab\ne 9
ab
=
9
.
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