Complex Numbers And Quadratic Equations question 712
Question: If the roots of the equation $ ax^{2}-bx+c=0 $ are $ \alpha ,\beta $ then the roots of the equation $ b^{2}cx^{2}-ab^{2}x+a^{3}=0 $ are
Options:
A) $ \frac{1}{{{\alpha }^{3}}+\alpha \beta },\frac{1}{{{\beta }^{3}}+\alpha \beta } $
B) $ \frac{1}{{{\alpha }^{2}}+\alpha \beta },\frac{1}{{{\beta }^{2}}+\alpha \beta } $
C) $ \frac{1}{{{\alpha }^{4}}+\alpha \beta },\frac{1}{{{\beta }^{4}}+\alpha \beta } $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Multiplying the second equation by $ \frac{c}{a^{3}} $ , we get $ \frac{b^{2}c^{2}}{a^{3}}x^{2}-\frac{b^{2}c}{a^{2}}x+c=0 $
$ \Rightarrow a{{( \frac{bc}{a^{2}}x )}^{2}}-b( \frac{bc}{a^{2}} )x+c=0 $
$ \Rightarrow \frac{bc}{a^{2}}x=\alpha ,\beta $
$ \Rightarrow (\alpha +\beta )\alpha \beta x=\alpha ,\beta $
$ \Rightarrow x=\frac{1}{(\alpha +\beta )\alpha },\frac{1}{(\alpha +\beta )\beta } $
BETA
