MathDB
Problems
Contests
Undergraduate contests
Brazil Undergrad MO
2018 Brazil Undergrad MO
15
15
Part of
2018 Brazil Undergrad MO
Problems
(1)
probability that all roots
Source: Brazil Undergrad MO - Galois-Noether 2018 #15
11/26/2019
A real number
t
o
to
t
o
is randomly and uniformly chosen from the
[
ā
3
,
4
]
[- 3,4]
[
ā
3
,
4
]
interval. What is the probability that all roots of the polynomial
x
3
+
a
x
2
+
a
x
+
1
x ^ 3 + ax ^ 2 + ax + 1
x
3
+
a
x
2
+
a
x
+
1
are real?
probability
Brazilian Math Olympiad
college contests
algebra