Complex Numbers And Quadratic Equations question 169
Question: If the equation $ x^{2}+\lambda x+\mu =0 $ has equal roots and one root of the equation $ x^{2}+\lambda x-12=0 $ is 2, then $ (\lambda ,\mu ) $ =
Options:
A) (4, 4)
B) (-4,4)
C) $ (4,-4) $
D) $ (-4,-4) $
Show Answer
Answer:
Correct Answer: A
Solution:
We have equal roots, therefore $ {{\lambda }^{2}}=4\mu $ . Now second equation $ x^{2}+\lambda x-12=0 $ has a root 2, so put $ x=2 $
Þ $ 4+2\lambda -12=0 $
Þ $ \lambda =4 $ Hence from $ {{\lambda }^{2}}=4\mu $ , we have $ \mu =\frac{16}{4}=4 $
Þ $ (\lambda ,\mu )=(4,4) $ .
BETA
