Question

Three roots of the equation, $x ^4- px ^3+ qx ^2- rx + s =0$ are $\tan A , \tan B$ and $\tan C$ where $A , B , C$ are the angles of a triangle. The fourth root of the biquadratic is :

• A. $\frac{p-r}{1-q+s}$
• B. $\frac{p-r}{1+q-s}$
• C. $\frac{p+r}{1-q+s}$
• D. $\frac{p+r}{1+q-s}$

Answer 1

Answer: (A)

Let the fourth root be tan D
Now $\tan (\Sigma A)=\frac{\Sigma \tan A-\Sigma \tan A \tan B \tan C}{1-\Sigma \tan A \tan B+\Pi \tan A} \quad \tan D=\frac{p-r}{1-q+s}$