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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
9.2
x^3 + ax^2 + bx + c = 0 (VI Soros Olympiad 1990-00 R2 9.2)
x^3 + ax^2 + bx + c = 0 (VI Soros Olympiad 1990-00 R2 9.2)
Source:
May 28, 2024
algebra
polynomial
Problem Statement
Can the equation
x
3
+
a
x
2
+
b
x
+
c
=
0
x^3 + ax^2 + bx + c = 0
x
3
+
a
x
2
+
b
x
+
c
=
0
have only negative roots , if we know that
a
+
2
b
+
4
c
=
−
1
2
a+2b+4c=- \frac12
a
+
2
b
+
4
c
=
−
2
1
?
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