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Byju's Answer
Standard XII
Mathematics
Inequalities Involving Mathematical Means
If AM and GM ...
Question
If AM and GM of roots of a quadratic equation are 8 and 5 respectively, then obtain the quadratic equation.
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Solution
Let
the
roots
of
the
quadratic
equation
be
a
and
b
.
AM
=
8
∴
a
+
b
2
=
8
⇒
a
+
b
=
16
.
.
.
.
.
.
.
.
(
i
)
Also
,
G
=
5
⇒
a
b
=
5
⇒
a
b
=
5
2
⇒
a
b
=
25
.
.
.
.
.
.
.
.
(
ii
)
Now
,
the
quadratic
equation
is
given
by
x
2
-
(
a
+
b
)
x
+
a
b
=
0
⇒
x
2
-
16
x
+
25
=
0
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