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1985 Bulgaria National Olympiad
Problem 2
sextic has only real roots
sextic has only real roots
Source: Bulgaria 1985 P2
June 16, 2021
algebra
Polynomials
Problem Statement
Find all real parameters
a
a
a
for which all the roots of the equation
x
6
+
3
x
5
+
(
6
−
a
)
x
4
+
(
7
−
2
a
)
x
3
+
(
6
−
a
)
x
2
+
3
x
+
1
x^6+3x^5+(6-a)x^4+(7-2a)x^3+(6-a)x^2+3x+1
x
6
+
3
x
5
+
(
6
−
a
)
x
4
+
(
7
−
2
a
)
x
3
+
(
6
−
a
)
x
2
+
3
x
+
1
are real.
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