Complex Numbers And Quadratic Equations question 661
Question: If $ \lambda \ne \mu $ and $ {{\lambda }^{2}}=5\lambda -3, $ $ {{\mu }^{2}}=5\mu -3, $ then the equation whose roots are $ \frac{\lambda }{\mu } $ and $ \frac{\mu }{\lambda } $ is
Options:
A) $ x^{2}-5x+3=0 $
B) $ 3x^{2}+19x+3=0 $
C) $ 3x^{2}-19x+3=0 $
D) $ x^{2}+5x-3=0 $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \lambda $ and $ \mu $ are the roots of $ {x^{2}} = 5x- 3 or x^{2}- 5x+3=0 $
$ \therefore \lambda +\mu =5and\lambda \mu =3 $ $ \frac{\lambda }{\mu }+\frac{\mu }{\lambda }=\frac{{{(\lambda +\mu )}^{2}}-2\lambda \mu }{\lambda \mu }=\frac{19}{3} $ $ \frac{\lambda }{\mu }.\frac{\mu }{\lambda }=1 $
$ \therefore Desired equation is x^{2}-\frac{19}{3} x+1=0 $ or $ 3x^{2}-19x+3=0 $
BETA
