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Byju's Answer
Standard X
Mathematics
Solving a Quadratic Equation by Factorization Method
If α ,β be ...
Question
I
f
α
,
β
b
e
t
h
e
r
o
o
t
s
o
f
t
h
e
e
q
u
a
t
i
o
n
a
x
2
+
b
x
+
c
=
0
t
h
e
n
t
h
e
v
a
l
u
e
o
f
−
a
α
2
b
α
+
c
+
−
a
β
2
b
β
+
c
i
s
e
q
u
a
l
t
o
Open in App
Solution
H
e
r
e
,
α
a
n
d
β
a
r
e
r
o
o
t
s
o
f
t
h
e
e
q
u
a
t
i
o
n
a
x
2
+
b
x
+
c
=
0
∴
α
+
β
=
−
b
a
&
α
β
=
c
a
⇒
a
α
+
a
β
=
−
b
&
a
α
β
=
c
a
α
2
b
α
+
c
+
a
β
2
b
β
+
c
=
a
α
2
b
α
+
a
α
β
+
a
β
2
b
β
+
a
α
β
=
a
α
2
α
(
b
+
a
β
)
+
a
β
2
β
(
b
+
a
α
)
=
a
α
(
b
+
a
β
)
+
a
β
(
b
+
a
α
)
=
−
(
b
+
α
β
)
(
b
+
a
β
)
−
(
b
+
a
α
)
(
b
+
a
α
)
=
−
1
−
1
=
−
2
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Similar questions
Q.
If
a
x
2
+
b
x
+
c
=
0
has roots
α
and
β
then-
a
α
2
+
b
α
+
c
=
0
and
a
β
2
+
b
β
+
c
=
0
If
α
,
β
are the roots of
x
2
−
p
(
x
+
1
)
−
c
=
0
,
c
≠
1
, then
α
2
+
2
α
+
1
α
2
+
2
α
+
c
+
β
2
+
2
β
+
1
β
2
+
2
β
+
c
=
Q.
If
α
,
β
are roots of the equation
a
x
2
+
b
x
+
c
=
0
then evaluate
1
(
a
α
)
2
+
1
(
a
β
)
2
Q.
If
α
,
β
are the roots of the equation
a
x
2
+
b
x
+
c
=
0
, then the value of
(
a
α
2
+
c
)
(
a
α
+
b
)
+
(
a
β
2
+
c
)
(
a
β
+
b
)
is
Q.
A real number
α
is said to be the root of the quadratic equation
a
x
2
+
b
x
+
c
=
0
, if
a
α
2
+
b
α
+
c
=
0
Q.
If
c
≠
0
and
α
,
β
are the roots of the quadratic equation
a
x
2
+
b
x
+
c
=
0
, then value of
a
α
2
+
c
a
α
+
b
+
a
β
2
+
c
a
β
+
b
is
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