InterviewSolution
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InterviewSolution
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Given that `alpha,gamma`are roots of the equation `A x^2-4x+1=0,a n dbeta,delta`the roots of the equation of `B x^2-6x+1=0,`such that `alpha,beta,gamma,a n ddelta`are in H.P., thena.`A=3`b. `A=4``B=2`d. `B=8`A. `A=3`B. `A=4`C. `B=2`D. `B=8` |
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Answer» Since `alpha,beta, gamma` and `delta` are in HP hence `1/(alpha),1/(beta),1/(gamma)` and `1/(delta)` are in AP and they may be take as a `a-3d, a-d, a+d` and `a+3d`. Replaceing `x` by `1/x` we get the equation whose roots are `a-3d, a+d` is `x^(2)-4x+A=0` and equation whose roots are `a-d,a+3d` is `x^(2)-6x+B=0` then `(a-3d)+(a+d)=4implies2(a-d)=4` and `(a-d)+(a+3d)=6implies2(a+d)=6` `:.a=5/2` and `d=1/2` Now `A=(a-3d)(a+d)=(5/2-3/2)(5/2+1/2)=3` and `B=(a-d)(a+3d)(5/2-1/2)(5/2+3/2)=8` |
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