If `alpha` is the only real root of the equation `x^3 + bx^2 + cx + 1 = 0 (b < c)`, then the value of `tan^-1 alpha+ tan^-1 (alpha^-1)` is equal to :A. `(pi)/(2)`B. `-(pi)/(2)`C. 0D. non existent

If `alpha` is the only real root of the equation `x^3 + bx^2 + cx + 1

1.	If `alpha` is the only real root of the equation `x^3 + bx^2 + cx + 1 = 0 (b < c)`, then the value of `tan^-1 alpha+ tan^-1 (alpha^-1)` is equal to :A. `(pi)/(2)`B. `-(pi)/(2)`C. 0D. non existent
Answer» Let `f(x)=x^(3)+bx^(2)+cx+1` Then `f(0)=1 gt 0 and f(-1)=b-c lt 0` `rarr alpha lt 0` `rarr tan^(-1)((1)/(alpha))=-pi + cot^(-1)alpha` `rarr tan^(-1) alpha+tan^(-1)(1)/(alpha)=-pi + tan^(-1)alpha+cos^(-1)alpha` `rarr tan^(-1)alpha+tan^(-1)(1)/(alpha)=-pi++(pi)/(2)=-(pi)/(2)`

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