Complex Numbers And Quadratic Equations question 555
Question: If the roots of the equation $ ax^{2}+bx+c=0 $ are $ \alpha ,\beta $ , then the value of $ \alpha {{\beta }^{2}}+{{\alpha }^{2}}\beta +\alpha \beta $ will be [EAMCET 1980; AMU 1984]
Options:
A) $ \frac{c(a-b)}{a^{2}} $
B) 0
C) $ -\frac{bc}{a^{2}} $
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
$ \alpha +\beta =-\frac{b}{a} $ and $ \alpha \beta =\frac{c}{a} $ Now $ \alpha {{\beta }^{2}}+{{\alpha }^{2}}\beta +\alpha \beta =\alpha \beta (\beta +\alpha )+\alpha \beta $ $ =\alpha \beta (1+\alpha +\beta )=\frac{c}{a}{ 1+( -\frac{b}{a} ) }=\frac{c(a-b)}{a^{2}} $
BETA
