InterviewSolution
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InterviewSolution
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The ratio of the roots of the equation `ax^2+ bx+c =0` is same equation `Ax^2+ Bx + C =0`. If `D_1 and D_2` are the discriminants of `ax^2+bx +C= 0 and Ax^2+Bx+C=0` respectively, then `D_1 : D_2`A. `(a^(2))/(p^(2))`B. `(b^(2))/(q^(2))`C. `(c^(2))/(r^(2))`D. none of these |
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Answer» Correct Answer - B Let `alpha_(1), beta_(1)` be the roots of `ax^(2) + bx + c = 0 and alpha_(2), beta_(2)` be the roots of `px^(2) + qx + r = 0`. Then, `(alpha_(1))/(beta_(1))=(alpha_(2))/(beta_(2))" "["Given"]` `rArr" "(alpha_(1)+beta_(1))/(alpha_(1)-beta_(1))=(alpha_(2)+beta_(2))/(alpha_(2)-beta_(2))" "[{:("Applying componendo"),(" ""and dividendo"):}]` `(alpha_(1)+beta_(1))^(2)/((alpha_(1)-beta_(1))^(2))=((alpha_(2)+beta_(2))^(2))/((alpha_(2)-beta_(2))^(2))` `rArr" "((alpha_(1)+beta_(1))^(2))/((alpha_(1)+beta_(1))^(2)4 alpha_(1)beta_(1))=((a_(2)+beta_(2))^(2))/((a_(2)+beta_(2))^(2)-4 alpha_(2) beta_(2))` `rArr" "(b^(2)//a^(2))/((b^(2)-4ac)/(a^(2)))=(q^(2)//p^(2))/((q^(2)-4rp)/(p^(2))) rArr (b^(2))/(D_(1))=(q^(2))/(D_(2))rArr (D_(1))/(D_(2))=(b^(2))/(q^(2))` |
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