Complex Numbers And Quadratic Equations question 2
Question: If a root of the equations $ x^{2}+px+q=0 $ and $ x^{2}+\alpha x+\beta =0 $ is common, then its value will be (where $ p\ne \alpha $ and $ q\ne \beta $ ) [IIT 1974, 1976; RPET 1997]
Options:
A) $ \frac{q-\beta }{\alpha -p} $
B) $ \frac{p\beta -\alpha q}{q-\beta } $
C) $ \frac{q-\beta }{\alpha -p} $ or $ \frac{p\beta -\alpha q}{q-\beta } $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let the common root be y. Then $ y^{2}+py+q=0 $ and $ y^{2}+\alpha y+\beta =0 $ On solving by cross multiplication, we have $ \frac{y^{2}}{p\beta -q\alpha }=\frac{y}{q-\beta }=\frac{1}{\alpha -p} $ \ $ y=\frac{q-\beta }{\alpha -p} $ and $ \frac{y^{2}}{y}=y=\frac{p\beta -q\alpha }{q-\beta } $
BETA
