A) \[a,5\]
B) \[b,5\]
C) \[a,\alpha \]
D) \[a,\beta \]
E) \[a,b\]
Correct Answer: E
Solution :
\[\because \]\[\alpha \]and\[\beta \]are the roots of equation \[(x-a)(x-b)=5,\]then \[\alpha +\beta =(\alpha +\beta )\]and\[\alpha \text{ }\beta =ab-5\] \[\therefore \] \[(x-\alpha )(x-\beta )+5=0\] \[\Rightarrow \]\[{{x}^{2}}-(\alpha +\beta )x+\alpha \beta +5=0\] \[\Rightarrow \]\[{{x}^{2}}-(a+b)x+ab-5+5=0\] \[\Rightarrow \] \[(x-a)(x-b)=0\] Hence, a and b are roots of equation \[(x-\alpha )(x-\beta )+5=0\]
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