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

Dear student, a 2 - 10acx - 11d = 0 c 2 - 10acx - 11b = 0 subtract them ...... a 2 - c 2 = 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. ........... a 2 + c 2 - 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

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

pranshu aggarwal, 11 years ago

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

Approved

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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

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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

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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