Complex Numbers And Quadratic Equations question 531
Question: If the sum of the roots of the equation $ ax^{2}+bx+c=0 $ be equal to the sum of their squares, then
Options:
A) $ a(a+b)=2bc $
B) $ c(a+c)=2ab $
C) $ b(a+b)=2ac $
D) $ b(a+b)=ac $
Show Answer
Answer:
Correct Answer: C
Solution:
Let $ \alpha $ and $ \beta $ be two roots of $ ax^{2}+bx+c=0 $ Then $ \alpha +\beta =-\frac{b}{a} $ and $ \alpha \beta =\frac{c}{a} $
Þ $ {{\alpha }^{2}}+{{\beta }^{2}}={{(\alpha +\beta )}^{2}}-2\alpha \beta =\frac{b^{2}}{a^{2}}-2\frac{c}{a} $ So under condition $ \alpha +\beta =a^{2}+{{\beta }^{2}} $
Þ $ -\frac{b}{a}=\frac{b^{2}-2ac}{a^{2}} $
Þ $ b(a+b)=2ac $ .
BETA
