Question

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​

Answer 1

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