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2014 AIME Problems
9
Roots of a cubic
Roots of a cubic
Source: 2014 AIME I #9
March 14, 2014
algebra
polynomial
Vieta
AMC
AIME
quadratics
trigonometry
Problem Statement
Let
x
1
<
x
2
<
x
3
x_1<x_2<x_3
x
1
<
x
2
<
x
3
be three real roots of equation
2014
x
3
−
4029
x
2
+
2
=
0
\sqrt{2014}x^3-4029x^2+2=0
2014
x
3
−
4029
x
2
+
2
=
0
. Find
x
2
(
x
1
+
x
3
)
x_2(x_1+x_3)
x
2
(
x
1
+
x
3
)
.
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