Complex Numbers And Quadratic Equations question 5
Question: If every pair of the equations $ x^{2}+px+qr=0 $ , $ x^{2}+qx+rp=0, $ $ x^{2}+rx+pq=0 $ have a common root, then the sum of three common roots is
Options:
A) $ \frac{-(p+q+r)}{2} $
B) $ \frac{-p+q+r}{2} $
C) $ -(p+q+r) $
D) $ -p+q+r $
Show Answer
Answer:
Correct Answer: A
Solution:
Let the roots be $ \alpha ,\beta ;\beta ,\gamma $ and $ \gamma ,\alpha $ respectively.
$ \therefore \alpha +\beta =-p,\ \beta +\gamma =-q,\gamma +\alpha =-r $ Adding all, we get $ \Sigma \alpha =-(p+q+r)/2 $ etc.
BETA
