A) \[\frac{3}{2}\]and\[\frac{3}{2}\]
B) \[\frac{7}{2}\]and\[\frac{7}{2}\]
C) \[\frac{5}{2}\]and\[\frac{5}{2}\]
D) None of these
Correct Answer: C
Solution :
Given \[4{{x}^{2}}-20x+25=0\] \[\Rightarrow \]\[\frac{1}{x}-\frac{3}{4}+\frac{1}{2+x}=0\] \[\Rightarrow \]\[(5,4)\] \[\Rightarrow \]\[\left( -\frac{4}{3},2 \right)\] \[\Rightarrow \] \[2x-5=0\] or \[2x-5=0\] \[\Rightarrow \] \[x=\frac{5}{2}\] or \[x=\frac{5}{2}\] \[\therefore \] The quadratic equation has equal roots \[{{a}_{0}}+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}}\] and \[{{a}_{0}},{{a}_{1}},{{a}_{2}}......{{a}_{n}}\].
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