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National and Regional Contests
Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 2
2016 Nigerian Senior MO Round 2
Problem 8
Polynomials and manipulating roots
Polynomials and manipulating roots
Source: 2016 Nigerian Senior MO Round 2
November 16, 2022
algebra
polynomial
Problem Statement
If
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
are the solutions of the equation
x
4
−
k
x
−
15
=
0
x^4-kx-15=0
x
4
−
k
x
−
15
=
0
, find the equation whose solutions are
a
+
b
+
c
d
2
,
a
+
b
+
d
c
2
,
a
+
c
+
d
b
2
,
b
+
c
+
d
a
2
\frac{a+b+c}{d^2}, \frac{a+b+d}{c^2}, \frac{a+c+d}{b^2}, \frac{b+c+d}{a^2}
d
2
a
+
b
+
c
,
c
2
a
+
b
+
d
,
b
2
a
+
c
+
d
,
a
2
b
+
c
+
d
.
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