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2020-21 IOQM India
11
IOQM 2021 P11 common zeroes
IOQM 2021 P11 common zeroes
Source:
January 17, 2021
algebra
common zero
Problem Statement
Let
X
=
{
−
5
,
−
4
,
−
3
,
−
2
,
−
1
,
0
,
1
,
2
,
3
,
4
,
5
}
X = \{-5,-4,-3,-2,-1,0,1,2,3,4,5\}
X
=
{
−
5
,
−
4
,
−
3
,
−
2
,
−
1
,
0
,
1
,
2
,
3
,
4
,
5
}
and
S
=
{
(
a
,
b
)
∈
X
×
X
:
x
2
+
a
x
+
b
and
x
3
+
b
x
+
a
have at least a common real zero .
}
S = \{(a,b)\in X\times X:x^2+ax+b \text{ and }x^3+bx+a \text{ have at least a common real zero .}\}
S
=
{(
a
,
b
)
∈
X
×
X
:
x
2
+
a
x
+
b
and
x
3
+
b
x
+
a
have at least a common real zero .
}
How many elements are there in
S
S
S
?
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