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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
9.3
x^2 + bx + c has 2 roots in (2,3) (VI Soros Olympiad 1990-00 R1 9.3)
x^2 + bx + c has 2 roots in (2,3) (VI Soros Olympiad 1990-00 R1 9.3)
Source:
May 27, 2024
algebra
inequalities
Problem Statement
The quadratic trinomial
x
2
+
b
x
+
c
x^2 + bx + c
x
2
+
b
x
+
c
has two roots belonging to the interval
(
2
,
3
)
(2, 3)
(
2
,
3
)
. Prove that
5
b
+
2
c
+
12
<
0
5b+2c+12 < 0
5
b
+
2
c
+
12
<
0
.
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