A) \[{{x}^{2}}-5x+3=0\]
B) \[3{{x}^{2}}+19x+3=0\]
C) \[3{{x}^{2}}-19x+3=0\]
D) \[{{x}^{2}}+5x-3=0\]
Correct Answer: C
Solution :
\[\lambda \] and \[\mu \] are the roots of \[{{\operatorname{x}}^{2}} = 5x- 3 \,or \,{{x}^{2}}- 5x+3=0\] \[\therefore \,\,\,\,\,\lambda +\mu =5\,\,and\,\,\lambda \mu =3\] \[\frac{\lambda }{\mu }+\frac{\mu }{\lambda }=\,\,\frac{{{(\lambda +\mu )}^{2}}-2\lambda \mu }{\lambda \mu }=\frac{19}{3}\] \[\frac{\lambda }{\mu }.\frac{\mu }{\lambda }\,\,=\,\,1\] \[\therefore \,\,\,\operatorname{Desired} equation is {{x}^{2}}-\frac{19}{3} x+1=0\] or \[3{{x}^{2}}-19x+3=0\]
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