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AP EAMCET Engineering 18 Sep 2020 Shift 1 Paper
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© examsnet.com
Question : 9
Total: 160
If the sum of the roots of the quadratic equations is
1
and sum of the squares of the roots is
13
, then find that equation
x
2
+
x
−
6
=
0
x
2
−
x
+
6
=
0
x
2
−
x
−
6
=
0
x
2
+
x
+
6
=
0
Validate
Solution:
Let the roots of the quadratic equation are
α
and
β
then it is given that
α
+
β
=
1
and
α
2
+
β
2
=
13
∴
α
β
=
1
2
[
(
α
+
β
)
2
−
(
α
2
+
β
2
)
]
=
1
2
[
1
−
13
]
=
−
6
So, equation of required quadratic is
x
2
−
(
α
+
β
)
x
+
α
β
=
0
⇒
x
2
−
x
−
6
=
0
© examsnet.com
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