দ্বিঘাত সমীকরণ x²+px+q এর দুটি মুল Tan 30^o ও Tan 15^o হলে 2+q-p এর মান-

$\begin{array}{l}\text { Given equation is } x^{2}+p x+q=0 \\ \text { Sum of roots }=\tan 30^{\circ}+\tan 15^{\circ}=-\mathrm{p} \\ \text { Product of roots }=\tan 30^{\circ} \cdot \tan 15^{\circ}=\mathrm{q} \\ \tan 45^{\circ}=\frac{\tan 30^{\circ}+\tan 15^{\circ}}{1-\tan 30^{\circ} \cdot \tan 15^{\circ}}=\frac{-p}{1-q}=1 \\ \Rightarrow-p=1-q \\ \Rightarrow q-p=1 \\.\\ \therefore 2+q-p=3\end{array}$