Complex Numbers And Quadratic Equations question 533
Question: If $ \alpha ,\beta $ be the roots of the equation $ x^{2}-2x+3=0 $ , then the equation whose roots are $ \frac{1}{{{\alpha }^{2}}} $ and $ \frac{1}{{{\beta }^{2}}} $ is
Options:
A) $ x^{2}+2x+1=0 $
B) $ 9x^{2}+2x+1=0 $
C) $ 9x^{2}-2x+1=0 $
D) $ 9x^{2}+2x-1=0 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \alpha ,\beta $ be the roots of $ x^{2}-2x+3=0 $ , then $ \alpha +\beta =2 $ and $ \alpha \beta =3 $ . Now required equation whose roots are $ \frac{1}{{{\alpha }^{2}}},\frac{1}{{{\beta }^{2}}} $ is $ x^{2}-( \frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}} )x+\frac{1}{{{\alpha }^{2}}{{\beta }^{2}}}=0 $
Þ $ x^{2}-( -\frac{2}{9} )x+\frac{1}{9}=0 $
Þ $ 9x^{2}+2x+1=0 $ .
BETA
