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If c,d are roots of X^2-10ax-11b=0 and a,b are roots of x^2-10ax-11b=0 and a,b are root of x^2-10cx-11d=0 , then value of a+b+c+d is

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Solution: $c+d=10a$ $.........(1)$ and $a+b=10c$ $...........(2)$

Subtracting $(1)$ from $(2)$ We get

$(a-c)+(b-d)=10(c-a)$

$Rightarrow$ $b-d=11(c-a)$ $...........(3)$

As $c$ is a root of $x^2-10ax-11b=0$

We get

$c^2-10ac-11b=0$ $...........(4)$

$a^2-10ac-11d=0$ $..............(5)$

Subtracting $(5)$ from $(4)$ ,we get

$Rightarrow$ $c^2-a^2=11(b-d)$

$Rightarrow$ $(c-a)(c+a)=(11)(11)(c-a)$

$Rightarrow$ $(c+a)=121$

$herefore$ $a+b+c+d=10(a+c)=10(121)=1210$

Posted by

Deependra Verma

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