Determinants Matrices Question 9
Question: If $ f(x)=a+bx+cx^{2} $ and $ \alpha ,\beta ,\gamma $ are the roots of the equation $ x^{3}=1, $ then is equal to
Options:
A) $ f(\alpha )+f(\beta )+f(\gamma ) $
B) $ f(\alpha )f(\beta )+f(\beta )f(\gamma )+f(\gamma )f(\alpha ) $
C) $ f(\alpha )f(\beta )f(\gamma ) $
D) $ f(\alpha )f(\beta )f(\gamma ) $
Show Answer
Answer:
Correct Answer: B
Solution:
- [d] $=-(a^{3}+b^{3}+c^{3}-abc) $
$ =-(a+b+c)(a+b{{\omega }^{2}}+c\omega ) $
$ (a+b\omega +c{{\omega }^{2}}) $ (Where $ \omega $ is cube roots of unity) $ [\therefore \alpha =1,\beta =\omega ,\gamma ={{\omega }^{2}}] $
$ =-f(\alpha )f(\beta )f(\gamma ) $
BETA
