The roots of the equation
[tex]x ^ 5 - 40x ^ 4 + Px ^ 3 + Qx ^ 2 + Rx + S = 0[/tex]
are in geometric progression. The sum of their reciprocals is 10. Find the value of |S|, where | | represent modulus function.
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[tex]x ^ 5 - 40x ^ 4 + Px ^ 3 + Qx ^ 2 + Rx + S = 0[/tex]
are in geometric progression. The sum of their reciprocals is 10. Find the value of |S|, where | | represent modulus function.
Please no spam
Thanks ✨
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Answer:
Let the roots be a,ar,ar
2
,ar
3
andar
4
. Then
a+ar+ar
2
+ar
3
+ar
4
=40
i.e. a(
r−1
r
5
−1
)=40
Also
a
1
+
ar
1
+
ar
2
1
+
ar
3
1
+
ar
4
1
=10
i.e
a
2
r
4
1
(r−1)
a(r
5
−1)
=10⇒a
2
r
4
=4
⇒ar
2
=±2
∴S=−a
5
r
10
=−(±2)
5
=±32
Answer:
Supposetherootsare
r
2
a
,
r
a
,a,ar,ar
2
SoS=a
5
and
r
2
a
+
r
a
+a+ar+ar
2
=40
Sumofreciprocalsare10
a
1
(
a
40
)=10
a=±2
So∣S∣=32
Step-by-step explanation:
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