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German National Olympiad
1996 German National Olympiad
6a
6a
Part of
1996 German National Olympiad
Problems
(1)
p(x) = x^3 + Ax^2 + Bx +C has 3 roots, at least 2 distinct then A^2+B^2+18C>0
Source: Germany 1996 p6a
2/22/2020
Prove the following statement: If a polynomial
p
(
x
)
=
x
3
+
A
x
2
+
B
x
+
C
p(x) = x^3 + Ax^2 + Bx +C
p
(
x
)
=
x
3
+
A
x
2
+
B
x
+
C
has three real positve roots at least two of which are distinct, then
A
2
+
B
2
+
18
C
>
0
A^2 +B^2 +18C > 0
A
2
+
B
2
+
18
C
>
0
.
polynomial
roots
algebra