If 'α' is the only real root of the equation x3+bx2+cx+1=0(b+c) , then the value of tan-1(α)+ tan-1(α-1) is equal to

Question

If 'α' is the only real root of the equation x3+bx2+cx+1=0(b+c) , then the value of tan-1(α)+ tan-1(α-1) is equal to (A) -(π/2) (B) (π/2) (C) 0 (D) cannot be determined

Tardigrade Admin · Accepted Answer

Let f(x) = x3+bx2 +cx+1 ∴ f(0) = 1>, f(-1)= b-c <0 ∴ -1 < α < 0 and ∴ tan-1(α) +tan-1 (1/α) = -(π/2)

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

$- \frac{π}{2}$

$\frac{π}{2}$

0

cannot be determined

Let $f (x) = x^{3} + b x^{2} + c x + 1$
$∴ f (0) = 1 >, f (- 1) = b - c < 0$
$∴ - 1 < α < 0$ and
$∴ t a n^{- 1} (α) + t a n^{- 1} \frac{1}{α} = - \frac{π}{2}$

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

−2π​

2π​

0

cannot be determined

Let f(x)=x3+bx2+cx+1 ∴f(0)=1>,f(−1)=b−c<0 ∴−1<α<0 and ∴tan−1(α)+tan−1α1​=−2π​

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

$- \frac{π}{2}$

$\frac{π}{2}$

Let $f (x) = x^{3} + b x^{2} + c x + 1$
$∴ f (0) = 1 >, f (- 1) = b - c < 0$
$∴ - 1 < α < 0$ and
$∴ t a n^{- 1} (α) + t a n^{- 1} \frac{1}{α} = - \frac{π}{2}$