Complex Numbers And Quadratic Equations question 578
Question: If $ \alpha ,\beta $ are the roots of $ ax^{2}+bx+c=0 $ , then the equation whose roots are $ 2+\alpha ,2+\beta $ is [EAMCET 1994]
Options:
A) $ ax^{2}+x(4a-b)+4a-2b+c=0 $
B) $ ax^{2}+x(4a-b)+4a+2b+c=0 $
C) $ ax^{2}+x(b-4a)+4a+2b+c=0 $
D) $ ax^{2}+x(b-4a)+4a-2b+c=0 $
Show Answer
Answer:
Correct Answer: D
Solution:
We have $ \alpha +\beta =\frac{-b}{a} $ and $ \alpha \beta =\frac{c}{a} $ Now sum of the roots $ =2+\alpha +2+\beta =4-\frac{b}{a} $ and product of the roots $ =(2+\alpha )(2+\beta ) $ $ =4+\frac{c}{a}-\frac{2b}{a}=\frac{4a+c-2b}{a} $ Hence the required equation is $ x^{2}-x( 4-\frac{b}{a} )+\frac{4a+c-2b}{a}=0 $ or $ ax^{2}-x(4a-b)+4a+c-2b=0 $ or $ ax^{2}+x(b-4a)+4a-2b+c=0 $ .
BETA
