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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 3 Questions
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© examsnet.com
Question : 5
Total: 100
Let
α
and
β
be the roots of the equation
px
2
+
qx
−
r
=
0
, where
p
≠
0
. If
p
,
q
and
r
be the consecutive terms of a non-constant G.P and
1
α
+
1
β
=
3
4
, then the value of
(
α
−
β
)
2
is :
[1-Feb-2024 Shift 2]
80
9
9
20
3
8
Validate
Solution:
👈: Video Solution
p
x
2
+
q
x
−
r
=
0
p
=
A
,
q
=
A
R
,
r
=
A
R
2
A
x
2
+
A
R
x
A
R
2
=
0
x
2
+
R
x
−
R
2
=
0
∵
1
α
+
1
β
=
3
4
∴
α
+
β
α
β
=
3
4
⇒
−
R
−
R
2
=
3
4
⇒
R
=
4
3
(
α
−
β
)
2
=
(
α
+
β
)
2
−
4
α
β
=
R
2
−
4
(
−
R
2
)
=
5
(
16
9
)
=
80
∕
9
© examsnet.com
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