Complex Numbers And Quadratic Equations question 721
Question: The roots of the equation $ 3^{2x}-{{10.3}^{x}}+9 $ =0 are
Options:
A) 1, 2
B) 0, 2
C) 0, 1
D) 1, 3
Show Answer
Answer:
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.
BETA
