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Byju's Answer
Standard XII
Mathematics
Inequalities Involving Mathematical Means
Roots of x3 ...
Question
Roots of x
3
- 9x
2
+ kx - 24 = 0 are in A.P then find roots and K
Open in App
Solution
The
given
equation
is
:
x
3
-
9
x
2
+
kx
-
24
=
0
Since
,
the
roots
of
the
above
equation
are
in
AP
,
so
,
Let
a
-
d
,
a
and
a
+
d
are
the
roots
of
the
above
equation
.
Now
,
sum
of
the
roots
=
-
coefficient
of
x
2
coefficient
of
x
3
⇒
a
-
d
+
a
+
a
+
d
=
-
-
9
1
=
9
⇒
3
a
=
9
⇒
a
=
3
Now
,
product
of
roots
=
-
constant
term
coefficient
of
x
3
⇒
a
-
d
a
a
+
d
=
24
⇒
3
-
d
3
+
d
3
=
24
⇒
9
-
d
2
=
8
⇒
d
2
=
1
⇒
d
=
±
1
When
d
=
1
;
then
roots
are
:
2
,
3
,
4
Now
,
product
of
roots
taken
2
at
a
time
=
coefficient
of
x
coefficient
of
x
3
⇒
2
×
3
+
3
×
4
+
4
×
2
=
k
⇒
6
+
12
+
8
=
k
⇒
k
=
26
When
d
=
-
1
;
then
roots
are
:
4
,
3
,
2
Now
,
product
of
roots
taken
2
at
a
time
=
coefficient
of
x
coefficient
of
x
3
⇒
2
×
3
+
3
×
4
+
4
×
2
=
k
⇒
6
+
12
+
8
=
k
⇒
k
=
26
So
,
k
=
26
Suggest Corrections
0
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