InterviewSolution
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InterviewSolution
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If `alpha,beta`are the roots of `x^2+p x+q=0a n dgamma,delta`are the roots of `x^2+p x+r=0,`then `((alpha-gamma)(alpha-delta))/((beta-gamma)(beta-delta))=``1`b. `q`c. `r`d. `q+r`A. 1B. qC. rD. q + r |
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Answer» Correct Answer - 1 `alpha, beta` be the roots of `x^(2) + px + q = 0` `gamma, delta` be the roots of `x^(2) + px + r = 0` `alpha + beta = -p` `alphabeta = q` `gamma + delta = -p` `gamma delta = r` Now, `(alpha - gamma)(alpha - delta) = alpha^(2) - alpha(gamma + delta) + gammadelta` `= alpha^(2) - alpha(alpha + beta) = r` `= - alphabeta + r = -q + r` By symmetry `(beta - gamma) (beta - delta) = -q + r` Hence, `((alpha - gamma)(alpha - delta))/((beta - gamma)(beta - delta)) = 1` |
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