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UPSC CDS 1 2020 Math Paper
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© examsnet.com
Question : 22
Total: 100
If fix) is divided by (x - a)(x - f ) where
α
≠
β
, then what is the remainder ?
(
x
−
α
)
f
(
α
)
−
(
x
−
β
)
f
(
β
)
α
−
β
(
x
−
α
)
f
(
β
)
−
(
x
−
β
)
f
(
α
)
α
−
β
(
x
−
β
)
f
(
α
)
−
(
x
−
α
)
f
(
β
)
α
−
β
(
x
−
β
)
f
(
β
)
−
(
x
−
α
)
f
(
α
)
α
−
β
Validate
Solution:
👈: Video Solution
f
(
x
)
=
c
(
x
−
α
)
(
x
−
β
)
+
a
x
+
b
Required Remainder is
a
x
+
b
.
f
(
α
)
=
a
α
+
b
;
f
(
β
)
=
a
β
+
b
a
=
f
(
α
)
−
f
(
β
)
(
α
−
β
)
b
=
f
(
α
)
−
a
α
=
f
(
α
)
−
f
(
α
)
−
f
(
β
)
(
α
−
β
)
α
Solving the equations
a
x
+
b
=
(
x
−
β
)
(
f
(
α
)
−
(
x
−
α
)
(
f
(
β
)
)
α
−
β
© examsnet.com
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