Complex Numbers And Quadratic Equations question 7
Question: If the equation $ x^{2}+px+q=0 $ and $ x^{2}+qx+p=0 $ , have a common root, then $ p+q+1= $ [Orissa JEE 2002]
Options:
A) 0
B) 1
C) 2
D) - 1
Show Answer
Answer:
Correct Answer: A
Solution:
Let a is the common root, so $ {{\alpha }^{2}}+p\alpha +q=0 $ …..(i) and $ {{\alpha }^{2}}+q\alpha +p=0 $ ….(ii) from (i) - (ii),
$ \Rightarrow (p-q)\alpha +(q-p)=0 $
$ \Rightarrow \alpha =1 $ Put the value of $ \alpha $ in (i), $ p+q+1=0. $
BETA
