Question

If $\tan {25}^{\circ }$ and $\tan {20}^{\circ }$ are the roots of $x^2+2px+q=0$, then the value of $2p-q$ is equal to

• A. $-2$
• B. $-1$
• C. $0$
• D. $1$

Answer 1

The correct option is B $-1$

$\tan 45°=\tan (25°+20°)\Rightarrow 1=\frac{\tan 20°+\tan 25°}{1-\tan 20°\cdot \tan 25°}\Rightarrow 1-\tan 20°\cdot \tan 25°=\tan 20°+\tan 25°$
Now
$\because \tan 20°,\tan 25°$ are the roots of the equation $x^2+2px+q=0$
$\therefore \tan 20°+\tan 25°=-2p\cdots \left(1\right)\text{and}\tan 25°\cdot \tan 20°=q\cdots \left(2\right)$
From $\left(1\right)$ and $\left(2\right)$
$2p-q=-1$