Complex Numbers And Quadratic Equations question 623
Question: If the roots of the quadratic equation $ x^{2}+px+q=0 $ are $ \tan 30{}^\circ $ and $ \tan 15{}^\circ $ respectively, then the value of $ 2+q-p $ is
Options:
A) 2
B) 3
C) 0
D) 1
Show Answer
Answer:
Correct Answer: B
Solution:
Given equation is $ x^{2}+px+q=0 $ Sum of roots $ =\tan 30{}^\circ +\tan 15{}^\circ =-p $ Product of roots $ =\tan 30{}^\circ .\tan 15{}^\circ =q $ $ \tan 45{}^\circ =\frac{\tan 30{}^\circ +\tan 15{}^\circ }{1-\tan 30{}^\circ .\tan 15{}^\circ }=\frac{-p}{1-q}=1 $
$ \Rightarrow -p=1-q\Rightarrow q-p=1 $
$ \therefore 2+q-p=3 $
BETA
