Question

. Solve 18

3 + 81

2 + 121 + 60 = 0 given that one root is equal to half the

Sum of the remaining roots​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

18x  

3

+81x  

2

+121x+60=0

One root is the half of sum of remaining roots. So roots are in AP.

Let roots be α−β,α,α+β

Sum of roots =−  

18

81

​  

=3α

α=−  

2

3

​  

 

So one root is x=−  

2

3

​  

 

Dividing 18x  

3

+81x  

2

+121x+60=0 by x+  

2

3

​  

 we get 18x  

2

+54x+40

Hence other roots are given by 18x  

2

+54x+40=0

⟹9x  

2

+27x+20=0

x=  

2∗9

−27±  

27  

2

−(4∗9∗20)

​  

 

​  

=  

18

−27±3

​  

=−  

3

4

​  

,−  

3

5

​  

 

The roots are −  

2

3

​  

,−  

3

4

​  

,−  

3

5

​