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All-Russian Olympiad Regional Round
1995 All-Russian Olympiad Regional Round
10.5
min (a+b+c)/(b-a) All-Russian MO 1995 Regional (R4) 10.5
min (a+b+c)/(b-a) All-Russian MO 1995 Regional (R4) 10.5
Source:
August 26, 2024
algebra
inequalities
trinomial
Problem Statement
Consider all quadratic functions
f
(
x
)
=
a
x
2
+
b
x
+
c
f(x) = ax^2 +bx+c
f
(
x
)
=
a
x
2
+
b
x
+
c
with
a
<
b
a < b
a
<
b
and
f
(
x
)
≥
0
f(x) \ge 0
f
(
x
)
≥
0
for all
x
x
x
. What is the smallest possible value of the expression
a
+
b
+
c
b
−
a
\frac{a+b+c}{b-a}
b
−
a
a
+
b
+
c
?
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