if one root of 18 x cube + 81 X square + 1 21 X + 60 is equals to zero is equal to half life the sum of the other two then one of its root is please Urgently required
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Step-by-step explanation:
MATHS
Solve the equations:
18x
3
+81x
2
+121x+60=0, one root being half the sum of the other two.
December 27, 2019avatar
Sonakshi Dsouza
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ANSWER
18x
4
+81x
3
+121x+60=0
Let the roots of the equation be a,b,
2
a+b
S
1
=a+b+
2
a+b
=−
18
81
2
3a+3b
=−
2
9
⇒a+b=−3.....(i)
S
4
=ab(
2
a+b
)=−
18
60
ab(
2
−3
)=−
18
60
ab=
9
20
.....(ii)
substituting b from (i)
a(−3−a)=
9
20
a
2
+3a+
9
20
=0
9a
2
+27a+20=0
9a
2
+12a+15a+20=0
3a(3a+4)+5(3a+4)=0
(3a+4)(3a+5)=0
⇒a=−
3
4
,−
3
5
substituting a in (ii)
⇒b=−
3
5
,−
3
4
So the roots of the equation are −
3
5
,−
3
4
,−
2
3
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