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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 :

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Verified by Experts

The correct Answer is:
`-(pi)/(2)`
Let `f(x) = x^(3) + bx^(2) + cx + 1`
So, `f(0) = 1 gt 0`
`f(-1) = b - c lt 0`
So, `-1 lt alpha lt 0`,
`:. Tan^(-1) (alpha) + tan^(-1) ((1)/(alpha)) = -(pi)/(2)`
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