Question

If $\alpha$ is the only real root of the equation $x^3+b{x}^2+cx+1=0(b<c),$ then the value of $ta{n}^{-1}\alpha +ta{n}^{-1}\left(\frac{1}{\alpha }\right)$ is equal to

• A. $\frac{\pi }{2}$
• B. $-\frac{\pi }{2}$
• C. Non existent

Answer 1

The correct option is B $-\frac{\pi }{2}$

$f\left(0\right)>0,f(-1)<o\Rightarrow \alpha$ lies between -1 and 0 $ta{n}^{-1}\left(1/\alpha \right)=-\pi +co{t}^{-1}\alpha$