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5
Cubic Roots
Cubic Roots
Source:
December 21, 2005
algebra
polynomial
Problem Statement
Suppose that the roots of
x
3
+
3
x
2
+
4
x
ā
11
=
0
x^3+3x^2+4x-11=0
x
3
+
3
x
2
+
4
x
ā
11
=
0
are
a
,
b
,
a, b,
a
,
b
,
and
c
,
c,
c
,
and that the roots of
x
3
+
r
x
2
+
s
x
+
t
=
0
x^3+rx^2+sx+t=0
x
3
+
r
x
2
+
s
x
+
t
=
0
are
a
+
b
,
b
+
c
,
a+b, b+c,
a
+
b
,
b
+
c
,
and
c
+
a
.
c+a.
c
+
a
.
Find
t
.
t.
t
.
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