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Putnam
1952 Putnam
B3
Putnam 1952 B3
Putnam 1952 B3
Source:
May 30, 2022
Putnam
Problem Statement
Develop necessary and sufficient conditions that the equation
∣
0
a
1
−
x
a
2
−
x
−
a
1
−
x
0
a
3
−
x
−
a
2
−
x
−
a
3
−
x
0
∣
=
0
(
a
i
≠
0
)
\begin{vmatrix} 0 & a_1 - x & a_2 - x \\ -a_1 - x & 0 & a_3 - x \\ -a_2 - x & -a_3 - x & 0\end{vmatrix} = 0 \qquad (a_i \neq 0)
0
−
a
1
−
x
−
a
2
−
x
a
1
−
x
0
−
a
3
−
x
a
2
−
x
a
3
−
x
0
=
0
(
a
i
=
0
)
shall have a multiple root.
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