Complex Numbers And Quadratic Equations question 766
Question: If one of the roots of the equation $ x^{2}+ax+b=0 $ and $ x^{2}+bx+a=0 $ is coincident, then the numerical value of $ (a+b) $ is [IIT 1986; RPET 1992; EAMCET 2002]
Options:
A) 0
B) - 1
C) 2
D) 5
Show Answer
Answer:
Correct Answer: B
Solution:
If $ \alpha $ is the coincident root, then $ {{\alpha }^{2}}+a\alpha +b=0 $ and $ {{\alpha }^{2}}+b\alpha +a=0 $
Þ $ \frac{{{\alpha }^{2}}}{a^{2}-b^{2}}=\frac{\alpha }{b-a}=\frac{1}{b-a} $
Þ $ {{\alpha }^{2}}=-(a+b);\alpha =1\Rightarrow -(a+b)=1 $
Þ $ (a+b)=-1 $ .
BETA
