If \[\alpha ,\beta \] are the roots of the equation \[a{{x}^{2}}+bx+c=0\] then the equation whose roots are \[\alpha +\frac{1}{\beta }\]and \[\beta +\frac{1}{\alpha }\], is [RPET 1991]

\[ab{{x}^{2}}+(a+c)bx+{{(a+c)}^{2}}=0\]

\[ac{{x}^{2}}+(a+c)bx+{{(a+c)}^{2}}=0\]

\[ac{{x}^{2}}+(a+b)cx+{{(a+c)}^{2}}=0\]

If \[\alpha ,\beta \] are the roots of the equation \[a{{x}^{2}}+bx+c=

1.	If \[\alpha ,\beta \] are the roots of the equation \[a{{x}^{2}}+bx+c=0\] then the equation whose roots are \[\alpha +\frac{1}{\beta }\]and \[\beta +\frac{1}{\alpha }\], is [RPET 1991]
A.	\[ac{{x}^{2}}+(a+c)bx+{{(a+c)}^{2}}=0\]
B.	\[ab{{x}^{2}}+(a+c)bx+{{(a+c)}^{2}}=0\]
C.	\[ac{{x}^{2}}+(a+b)cx+{{(a+c)}^{2}}=0\]
D.	None of these
Answer» B. \[ab{{x}^{2}}+(a+c)bx+{{(a+c)}^{2}}=0\]

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If \[\alpha ,\beta \] are the roots of the equation \[a{{x}^{2}}+bx+c=0\] then the equation whose roots are \[\alpha +\frac{1}{\beta }\]and \[\beta +\frac{1}{\alpha }\], is [RPET 1991]

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