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Swedish Mathematical Competition
1979 Swedish Mathematical Competition
5
5
Part of
1979 Swedish Mathematical Competition
Problems
(1)
min a such that ax^2 - bx + c has two distinct zeros in the interval (0,1)
Source: 1979 Swedish Mathematical Competition p5
3/26/2021
Find the smallest positive integer
a
a
a
such that for some integers
b
b
b
,
c
c
c
the polynomial
a
x
2
ā
b
x
+
c
ax^2 - bx + c
a
x
2
ā
b
x
+
c
has two distinct zeros in the interval
(
0
,
1
)
(0,1)
(
0
,
1
)
.
algebra
trinomial