A) 1, 2
B) 0, 2
C) 0, 1
D) 1, 3
Correct Answer: B
Solution :
Given equation is \[{{3}^{2x}}-{{10.3}^{x}}+9=0\] can be written as \[{{({{3}^{x}})}^{2}}-10({{3}^{x}})+9=0\] Let \[a={{3}^{x}}\], then it reduces to the equation \[{{a}^{2}}-10a+9=0\,\,\,\Rightarrow (a-9)(a-1)=0\,\,\Rightarrow a=9,1\] Now \[a={{3}^{x}}\,\,\Rightarrow 9={{3}^{x}}\,\,\Rightarrow {{3}^{2}}={{3}^{x}}\,\,\Rightarrow x=2\] and \[1={{3}^{x}}\]\[\Rightarrow \,\,{{3}^{0}}={{3}^{x}}\,\,\Rightarrow x=0\]. Hence roots are 0, 2.
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