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Byju's Answer
Standard X
Mathematics
Solving a Quadratic Equation by Factorization Method
Using quadrat...
Question
Using quadratic formula solve the given quadratic equation
9
x
2
−
9
(
a
+
b
)
+
(
2
a
2
+
5
a
b
+
2
b
2
)
=
0
Open in App
Solution
We have
9
x
2
−
9
(
a
+
b
)
+
(
2
a
2
+
5
a
b
+
2
b
2
)
=
0
Comparing this equation with
A
x
2
+
B
x
+
C
=
0
we have
A
=
9
,
B
=
−
9
(
a
+
b
)
,
C
=
2
a
2
+
5
a
b
+
2
b
2
D
=
B
2
−
4
A
C
⇒
D
=
81
(
a
+
b
)
2
−
36
(
2
a
2
+
5
a
b
+
2
b
2
)
⇒
D
=
9
(
a
−
b
)
2
≥
0
So, the roots of the given equation are real and are given by
α
=
−
B
−
√
D
2
A
=
−
9
(
a
+
b
)
+
3
(
a
−
b
)
18
=
2
a
+
b
3
β
=
B
−
√
D
2
A
=
−
9
(
a
+
b
)
−
3
(
a
−
b
)
18
=
a
+
2
b
3
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0
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