A) \[2{{x}^{2}}+3x+18=0\]
B) \[{{x}^{2}}+6x-9=0\]
C) \[{{x}^{2}}+6x+9=0\]
D) \[{{x}^{2}}-6x+9=0\]
Correct Answer: C
Solution :
Given equation is \[9{{x}^{2}}+6x+1=0\] \[\Rightarrow \alpha +\beta =\frac{-6}{9}=\frac{-2}{3}\] and \[\alpha \beta =1/9\] \[\therefore \alpha -\beta =\sqrt{{{(\alpha +\beta )}^{2}}-4\alpha \beta }\] \[=\sqrt{\frac{4}{9}-4.\frac{1}{9}}=0\] \[\Rightarrow \alpha =\frac{-1}{3},\beta =\frac{-1}{3}\] \ Equation \[{{x}^{2}}-(\alpha +\beta )x+\alpha \beta =0\] \[\Rightarrow {{x}^{2}}+6x+9=0\].
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