If the roots of x^2+px+q=0 are 30^ and 15^ respectively, then the value of 2+q-p is

Question

If the roots of $x^2+px+q=0$ are $	an30^\circ$ and $	an15^\circ$ respectively, then the value of $2+q-p$ is

Accepted Answer

Sum $=\tan30^\circ+\tan15^\circ=-p$; product $=\tan30^\circ\tan15^\circ=q$.

$$\tan45^\circ=\frac{\tan30^\circ+\tan15^\circ}{1-\tan30^\circ\tan15^\circ}=\frac{-p}{1-q}=1 \implies -p=1-q \implies q-p=1.$$

$2+q-p=3.$

Solutions · 1