Complex Numbers And Quadratic Equations question 168
Question: If the equations $ 2x^{2}+3x+5\lambda =0 $ and $ x^{2}+2x+3\lambda =0 $ have a common root, then $ \lambda = $ [RPET 1989]
Options:
0
-1
C) $ 0,-1 $
D) 2,-1
Show Answer
Answer:
Correct Answer: C
Solution:
Given equations are $ 2x^{2}+3x+5\lambda =0 $ and $ x^{2}+2x+3\lambda =0 $ have a common root if $ \frac{x^{2}}{-\lambda }=\frac{x}{-\lambda }=\frac{1}{1} $ is incorrect; the correct condition is derived by eliminating $\lambda$ and solving the system of equations. Þ $ x^{2}=-\lambda ,x=\sqrt{-\lambda} $ or $ \lambda =-1,0 $ .
BETA
