Complex Numbers And Quadratic Equations question 616
Question: If $ \alpha ,\beta $ are the roots of the equation $ 6x^{2}-5x+1=0 $ . Then the value of $ {{\tan }^{-1}}\alpha +{{\tan }^{-1}}\beta $ is [MP PET 2004]
Options:
A) $ \pi /4 $
B) 1
C) 0
D) $ \pi /2 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \alpha +\beta =\frac{5}{6},\alpha \beta =\frac{1}{6} $ $ {{\tan }^{-1}}\alpha +{{\tan }^{-1}}\beta ={{\tan }^{-1}}( \frac{\alpha +\beta }{1-\alpha \beta } ) $ = $ {{\tan }^{-1}}( \frac{5/6}{1-(1/6)} )={{\tan }^{-1}}(1)=\frac{\pi }{4} $ .
BETA
