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Question

# If c,d are zeros of x2âˆ’10axâˆ’11b and a,b are zeros of x2âˆ’10cxâˆ’11d, 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 1210From properties of roots,a+b=10c - (1), c+d=10a - (2) , a.b=−11d & cd=−11bsubtracting (2) from (1) (x.c)+(b−d)=10(c−a)∴b−d=11(c−a) - (3)As a is root of x2−10cx−11d=0,a2−10ac−11d=0 - (4)Similarly, c2−10ca−11b=0 - (5)subtracting (4) from (5), c2−a2=11(b−d)∴(c+a)(c−a)=11×11(c−a) (from 3)∴c+a=121 Adding (1) & (2), a+b+c+d=10×121=1210

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