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Thailand National Olympiad
2010 Thailand Mathematical Olympiad
9
9
Part of
2010 Thailand Mathematical Olympiad
Problems
(1)
min real root of 2x^5 + 5x^4 + 5x^3 + ax^2 + bx + c = 0, given all roots reals
Source: 2010 Thailand Mathematical Olympiad day 1 p9
3/12/2021
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be real numbers so that all roots of the equation
2
x
5
+
5
x
4
+
5
x
3
+
a
x
2
+
b
x
+
c
=
0
2x^5 + 5x^4 + 5x^3 + ax^2 + bx + c = 0
2
x
5
+
5
x
4
+
5
x
3
+
a
x
2
+
b
x
+
c
=
0
are real. Find the smallest real root of the equation above.
polynomial
algebra