InterviewSolution
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InterviewSolution
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If the roots of the cubic equation `ax^3+bx^2+cx+d=0` are in G.P thenA. `c^(3)a=b^(3)d`B. `ca^(2)=bd^(3)`C. `a^(3)b=c^(3)d`D. `ab^(3)=cd^(3)` |
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Answer» Correct Answer - A Let `(A)/(R),A,AR` be the roots of the equation `ax^(3)+bx^(2)+cx+d=0` `:." Product of the roots "=-(d)/(a)`. `rArr" "A^(3)=-(d)/(a)A=-((d)/(a))^(1//3)` Since A is a root of the given equation. `:." "aA^(3)+bA^(2)+cA+d=0` `rArr" "a(-(d)/(a))+b(-(d)/(a))^(2//3)+c(-(d)/(a))^(1//3)+d=0` `rArr" "b((d)/(a))^(2//3)=c((d)/(a))^(1//3)rArrb^(3)xx(d)/(a)rArrb^(3)d=c^(3)a` |
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