Complex Numbers And Quadratic Equations question 526
Question: If $ \alpha $ and $ \beta $ are the roots of the equation $ 2x^{2}-3x+4=0 $ , then the equation whose roots are $ {{\alpha }^{2}} $ and $ {{\beta }^{2}} $ is
Options:
A) $ 4x^{2}+7x+16=0 $
B) $ 4x^{2}+7x+6=0 $
C) $ 4x^{2}+7x+1=0 $
D) $ 4x^{2}-7x+16=0 $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \alpha +\beta =\frac{3}{2} $ and $ \alpha \beta =2 $ $ {{\alpha }^{2}}+{{\beta }^{2}}={{(\alpha +\beta )}^{2}}-2\alpha \beta =\frac{9}{4}-4=-\frac{7}{4} $ Hence required equation $ x^{2}-({{\alpha }^{2}}+{{\beta }^{2}})x+{{\alpha }^{2}}{{\beta }^{2}}=0 $
Þ $ x^{2}+\frac{7}{4}x+4=0 $
Þ $ 4x^{2}+7x+16=0 $
BETA
