Complex Numbers And Quadratic Equations question 593
Question: If the sum of the roots of the equation $ x^{2}+px+q=0 $ is equal to the sum of their squares, then [Pb. CET 1999]
Options:
A) $ p^{2}-q^{2}=0 $
B) $ p^{2}+q^{2}=2q $
C) $ p^{2}+p=2q $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Let the roots be a and b
Þ $ \alpha +\beta =-p $ , $ \alpha \beta =q $ Given, $ \alpha +\beta ={{\alpha }^{2}}+{{\beta }^{2}} $ But $ \alpha +\beta ={{(\alpha +\beta )}^{2}}-2\alpha \beta $
$ \Rightarrow -p={{(-p)}^{2}}-2q $
$ \Rightarrow p^{2}-2q=-p $
$ \Rightarrow p^{2}+p=2q $ .
BETA
