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2013 CHMMC (Fall)
2
2013 CHMMC Tiebreaker 2 - roots of x^4 - 3x^2 + 6x - 12 = 1
2013 CHMMC Tiebreaker 2 - roots of x^4 - 3x^2 + 6x - 12 = 1
Source:
March 1, 2024
algebra
polynomial
CHMMC
Problem Statement
Suppose the roots of
x
4
−
3
x
2
+
6
x
−
12
=
1
x^4 - 3x^2 + 6x - 12 = 1
x
4
−
3
x
2
+
6
x
−
12
=
1
are
α
\alpha
α
,
β
\beta
β
,
γ
\gamma
γ
, and
δ
\delta
δ
. What is the value of
α
+
β
+
γ
δ
2
+
α
+
δ
+
γ
β
2
+
α
+
β
+
δ
γ
2
+
δ
+
β
+
γ
α
2
?
\frac{\alpha+ \beta+ \gamma }{\delta^2}+\frac{\alpha+ \delta+ \gamma}{\beta^2}+\frac{\alpha+ \beta+ \delta}{\gamma^2}+\frac{\delta+ \beta+ \gamma }{\alpha^2}?
δ
2
α
+
β
+
γ
+
β
2
α
+
δ
+
γ
+
γ
2
α
+
β
+
δ
+
α
2
δ
+
β
+
γ
?
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