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2004 Austria Beginners' Competition
3
3
Part of
2004 Austria Beginners' Competition
Problems
(1)
(m-2)x^2+(m^2-4m+3)x-(6m^2-2)=0 . sum X_i^3=0
Source: 2004 Austria Beginners' Competition p3
10/4/2022
Determine the value of the parameter
m
m
m
such that the equation
(
m
−
2
)
x
2
+
(
m
2
−
4
m
+
3
)
x
−
(
6
m
2
−
2
)
=
0
(m-2)x^2+(m^2-4m+3)x-(6m^2-2)=0
(
m
−
2
)
x
2
+
(
m
2
−
4
m
+
3
)
x
−
(
6
m
2
−
2
)
=
0
has real solutions, and the sum of the third powers of these solutions is equal to zero.
algebra
polynomial
sum of roots
Quadratic