Complex Numbers And Quadratic Equations question 814
Question: If $ \alpha ,\beta ,\gamma $ are the roots of the equation $ x^{3}+4x+1=0, $ then $ {{(\alpha +\beta )}^{-1}}+{{(\beta +\gamma )}^{-1}}+{{(\gamma +\alpha )}^{-1}}= $ [EAMCET 2003]
Options:
A) 2
B) 3
C) 4
D) 5
Show Answer
Answer:
Correct Answer: C
Solution:
Ifa, b, g are the roots of the equation. $ x^{3}-px^{2}+qx-r=0 $
$ \therefore {{(\alpha +\beta )}^{-1}}+{{(\beta +\gamma )}^{-1}}+{{(\gamma +\alpha )}^{-1}}=\frac{p^{2}+q}{pq-r} $ Given, $ p=0,q=4,r=-1 $
Þ $ \frac{p^{2}+q}{pq-r}=\frac{0+4}{0+1}=4 $ .
BETA
