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Question

If c,d are zeros of x210ax11b and a,b are zeros of x210cx11d, then value of a+b+c+d is :

A
1210
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B
1
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C
2530
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D
11
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Solution

The correct option is A 1210
From properties of roots,

a+b=10c - (1), c+d=10a - (2) , a.b=11d & cd=11b

subtracting (2) from (1) (x.c)+(bd)=10(ca)

bd=11(ca) - (3)

As a is root of x210cx11d=0,a210ac11d=0 - (4)

Similarly, c210ca11b=0 - (5)

subtracting (4) from (5), c2a2=11(bd)

(c+a)(ca)=11×11(ca) (from 3)

c+a=121 Adding (1) & (2), a+b+c+d=10×121

=1210

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