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If c, d are the roots of x 2 -10ax-11b=0 and a, b are the roots of x 2 -10cx-11d=0 then value of “a + b + c + d” is a) 1210 b) - 1 c) 2530 c) - 11


If c, d are the roots of x2-10ax-11b=0 and a, b are the roots of x2-10cx-11d=0 then value of “a + b + c + d” is


a) 1210                                                                      b) -1


c) 2530                                                                       c) -11


Grade:

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
11 years ago

Dear student,

a2 - 10acx - 11d = 0

c2 - 10acx - 11b = 0

 

subtract them ......

 

a2 - c2 = 11 ( d - b )    ........ (1)

 

a + b = 10c, ab = - 11d,

c + d = 10a, cd =  - 11b

 

a + b + c + d  = 10 ( a + c ) ...... (2)

b + d = 9 ( a + c ) ....... (3)

 

Also,   abcd = 121bd

so  ac = 121

 

from result (1) & (3)  ..... 

( b + d ) ( a - c ) / 9 = 11 ( d - b )

 ( a - c ) / 99 = ( d - b ) / ( b + d )

 

Simplifying. ...........

a2 + c2  - 20 ac - 11 ( b + d ) = 0

 

( a + c )2 - 22ac - 11 ( a + c ) 9 = 0

substutuing dat ac = 121

u get

finally

(a+c)2 - 99 (a+c) - 2662 = 0

 

This is a quadratic in a+c

solving u get

a  +  c = 121

 

 

Go to result  :::

 

a + b + c + d = 10 ( a + c )  = 1210

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