A) \[{{x}^{2}}-4=0\]
B) \[{{x}^{2}}-4x+6=0\]
C) \[{{x}^{2}}-5x+4=0\]
D) \[{{x}^{2}}-3x+2=0\]
E) \[{{x}^{2}}-x=0\]
Correct Answer: C
Solution :
\[{{4}^{1/2}},{{4}^{1/4}},{{4}^{1/8}},{{4}^{1/16}},.....\]are given roots, then Sum of roots \[={{4}^{1/2}}{{.4}^{1/4}}{{.4}^{1/8}},.....\] \[=5\] Product of roots \[={{4}^{1/2}}{{.4}^{1/4}}{{.4}^{1/8}}.....\] \[={{4}^{1/2+1/4+1/8+.....}}\] \[={{4}^{\frac{1/2}{1-1/2}}}=4\] \[\therefore \]Required equation is \[{{x}^{2}}\] (sum of roots) x + (product of roots) = 0 \[\Rightarrow \] \[{{x}^{2}}-5x+4=0\]
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