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Junior Tuymaada Olympiad
2005 Junior Tuymaada Olympiad
5
5
Part of
2005 Junior Tuymaada Olympiad
Problems
(1)
integer f(x) = x ^ 2 + ax + b, with f (x) >= - 9/ 10, Prove f (x)>= - 1/4
Source: Tuymaada Junior 2005 p5
5/12/2019
Given the quadratic trinomial
f
(
x
)
=
x
2
+
a
x
+
b
f (x) = x ^ 2 + ax + b
f
(
x
)
=
x
2
+
a
x
+
b
with integer coefficients, satisfying the inequality
f
(
x
)
≥
−
9
10
f (x) \geq - {9 \over 10}
f
(
x
)
≥
−
10
9
for any
x
x
x
. Prove that
f
(
x
)
≥
−
1
4
f (x) \geq - {1 \over 4}
f
(
x
)
≥
−
4
1
for any
x
x
x
.
quadratic trinomial
trinomial
algebra