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  1. #1
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    quadratic

    if the roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-11b=0 are c,d then find the value of a+b+c+d(a,b,c,d real distinct numbers)?


    (ans=1210)
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  2. #2
    Senior Member pankaj's Avatar
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    Quote Originally Posted by abhishek arora View Post
    if the roots of the equation x^2-10cx-11d=0 are a,b and those of x^2-10ax-11b=0 are c,d then find the value of a+b+c+d(a,b,c,d real distinct numbers)?


    (ans=4)
    Boy,your answer is surely wrong

    $\displaystyle a+b=10c$

    $\displaystyle c+d=10a$

    $\displaystyle a+b+c+d=10(a+c)$

    $\displaystyle b+d=9(a+c).$Also we have $\displaystyle a+b-c-d=10c-10a$.Thus, $\displaystyle b-d=11(c-a)$

    Since $\displaystyle a$ is root of $\displaystyle x^2-10cx-11d=0$,we have $\displaystyle a^2-10ac-11d=0$........(1)

    Since $\displaystyle c$is root of $\displaystyle x^2-10ax-11b=0$,we have $\displaystyle c^2-10ac-11b=0$.........(2)

    Subtracting (1) and (2)

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

    $\displaystyle (a+c)(c-a)=121(c-a)$

    $\displaystyle (a+c)=121$

    $\displaystyle a+b+c+d=10(a+c)=1210$
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