If α is the only real root of the equation x 3+ bx 2+ cx +1=0, then the value of tan -1 α+ tan -1((1/α)) is equal to

Question

If α is the only real root of the equation x 3+ bx 2+ cx +1=0, then the value of tan -1 α+ tan -1((1/α)) is equal to (A) 0 (B) (π/2) (C) (-π/2) (D) (3 π/2)

Tardigrade Admin · Accepted Answer

Θ f(0)=1 ∴ Only real root α<0 ∴ tan -1 α+(-π+ cot -1 α)=-π+(π/2)=(-π/2)

Q. If $α$ is the only real root of the equation $x^{3} + b x^{2} + c x + 1 = 0$ , then the value of $tan^{- 1} α + tan^{- 1} (\frac{1}{α})$ is equal to

0

$\frac{π}{2}$

$\frac{- π}{2}$

$\frac{3 π}{2}$

$Θ f (0) = 1$
$∴$ Only real root $α < 0$
$∴ tan^{- 1} α + (- π + cot^{- 1} α) = - π + \frac{π}{2} = \frac{- π}{2}$

Q. If α is the only real root of the equation x3+bx2+cx+1=0, then the value of tan−1α+tan−1(α1​) is equal to

0

2π​

2−π​

23π​

Θf(0)=1 ∴ Only real root α<0 ∴tan−1α+(−π+cot−1α)=−π+2π​=2−π​

Q. If $α$ is the only real root of the equation $x^{3} + b x^{2} + c x + 1 = 0$ , then the value of $tan^{- 1} α + tan^{- 1} (\frac{1}{α})$ is equal to

$\frac{π}{2}$

$\frac{- π}{2}$

$\frac{3 π}{2}$

$Θ f (0) = 1$
$∴$ Only real root $α < 0$
$∴ tan^{- 1} α + (- π + cot^{- 1} α) = - π + \frac{π}{2} = \frac{- π}{2}$