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Flanders Math Olympiad
2011 Flanders Math Olympiad
1
1
Part of
2011 Flanders Math Olympiad
Problems
(1)
cx^2 - bx + a >cx - b if ax^2+bx+c >cx
Source: Flanders Math Olympiad 2011 p1
12/24/2022
Given are three numbers
a
,
b
,
c
∈
R
−
{
0
}
a, b, c \in R-\{0\}
a
,
b
,
c
∈
R
−
{
0
}
. The parabola with equation
y
=
a
x
2
+
b
x
+
c
y = ax^2+bx+c
y
=
a
x
2
+
b
x
+
c
lies above the line
y
=
c
x
y = cx
y
=
c
x
. Prove that the parabola with equation
y
=
c
x
2
−
b
x
+
a
y = cx^2 - bx + a
y
=
c
x
2
−
b
x
+
a
lies above the line
y
=
c
x
−
b
y = cx - b
y
=
c
x
−
b
.
algebra
inequalities
trinomial