MathDB
Problems
Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2018 Korea Junior Math Olympiad
1
Quadratic function
Quadratic function
Source: KJMO 2018 p1
July 26, 2019
algebra
function
Problem Statement
Let
f
f
f
be a quadratic function which satisfies the following condition. Find the value of
f
(
8
)
−
f
(
2
)
f
(
2
)
−
f
(
1
)
\frac{f(8)-f(2)}{f(2)-f(1)}
f
(
2
)
−
f
(
1
)
f
(
8
)
−
f
(
2
)
.For two distinct real numbers
a
,
b
a,b
a
,
b
, if
f
(
a
)
=
f
(
b
)
f(a)=f(b)
f
(
a
)
=
f
(
b
)
, then
f
(
a
2
−
6
b
−
1
)
=
f
(
b
2
+
8
)
f(a^2-6b-1)=f(b^2+8)
f
(
a
2
−
6
b
−
1
)
=
f
(
b
2
+
8
)
.
Back to Problems
View on AoPS