Question

In a triangle ABC, if angle C is obtuse and angles A and B are given by roots of the equation tan2x + p tanx + q = 0, then the value of q is

• A. greater than 1
• B. less than 1
• C. equal to 1

Answer 1

The correct option is B less than 1

We have A + B = $\pi$ - C
$=\tan \left(A+B\right)=-\tan C$
$=\frac{\tan A+\tan B}{1-\tan A\cdot \tan B}>0$ $\left[\tan A>0,\tan B>0,\tan C<0\right]$
= $\tan A\cdot \tan B<1\Rightarrow q<1$