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National and Regional Contests
Greece Contests
Greece National Olympiad
1995 Greece National Olympiad
3
3
Part of
1995 Greece National Olympiad
Problems
(1)
ax^4+bx^3+cx^2+dx+e=0 has at least one real root [Greece 1995]
Source: Greece 1995
2/11/2009
If the equation
a
x
2
+
(
c
−
b
)
x
+
(
e
−
d
)
=
0
ax^2+(c-b)x+(e-d)=0
a
x
2
+
(
c
−
b
)
x
+
(
e
−
d
)
=
0
has real roots greater than
1
1
1
, prove that the equation
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
ax^4+bx^3+cx^2+dx+e=0
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
=
0
has at least one real root.
algebra unsolved
algebra