InterviewSolution
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InterviewSolution
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If the ratio of the roots of `x^2 + bx + c =0` and ` x^2 + qx + r = 0` is same then |
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Answer» Let `alpha,beta` are the roots of `x^2+bx+c = 0` Then, `alpha+beta =-b` and `alphabeta = c` Let `A,B` are the roots of `x^2+qx+r = 0` Then, `A+B =-q` and `AB = r` We are given, `alpha/beta = A/B->(1)` `=>beta/alpha = B/A->(2)` Adding (1) and (2), `alpha/beta+beta/alpha = A/B+B/A` `=>(alpha^2+beta^2)/(alphabeta) = (A^2+B^2)/(AB)` `=>((alpha+beta)^2-2alphabeta)/(alphabeta) = ((A+B)^2-2AB)/(AB)` `=>(b^2-2c)/c = (q^2-2r)/r` `=>b^2r-2cr = q^2c-2cr` `=>b^2r = q^2c` So, option `C` is the correct option. |
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