InterviewSolution
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InterviewSolution
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let `alpha,beta` be the roots of `x^2-x+p=0` and `gamma,delta` be the roots of `x^2-4x+q=0` . if `alpha,beta,gamma,delta` are in `G.P.` then the integral values of `p&q` respectively , are |
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Answer» given that eqn `x^2- x + p = 0` having roots `(alpha, beta)` `x^2 - 4*x +q = 0` having roots `(gamma, delta)` `alpha, beta, gamma, delta` are in GP terms will be as `a, a*r , ar^2, a*r^3` in GP `alpha + beta= 1 & gamma + delta = 4` `alpha*beta= p & gamma*delta= q` now, `a + a*r = 1` `a(1+r) = 1` eqn (1) `a^2*r = p` eqn (2) `a*r^2 + a*r^3 = 4` `a*r^2 *(1+r) = 4` eqn (3) `a^2*r^5= q` eqn (4) dividing eqn 3 by 1` (a*r^2*(r+1))/(a*(r+1)) = 4/1` `r^2 = 4` `r = +- 2` now, ` a(r+1) = 1` ` r= 2, a=1/3` `a= 1/(r+1) , r=-2, a=-1` `alpha= -1 , beta= 2, gamma = -4 , delta = 8` `alpha = 1/3 , beta = 2/3 , gamma = 4/3 , delta = 8/3` `p = alpha* beta = a*a*r = -2` `q= gamma* delta = -4*8 =-32` |
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