A) \[5{{x}^{2}}-16x+7\]= 0
B) \[7{{x}^{2}}-16x+5=0\]
C) \[7{{x}^{2}}-16x+8=0\]
D) \[3{{x}^{2}}-12x+7=0\]
Correct Answer: A
Solution :
Let the roots are a and b \[\Rightarrow \frac{\alpha +\beta }{2}=\frac{8}{5}\] \[\Rightarrow \alpha +\beta =\frac{16}{5}\] ?..(i) and \[\frac{\frac{1}{\alpha }+\frac{1}{\beta }}{2}=\frac{8}{7}\] \[\Rightarrow \frac{\alpha +\beta }{2\alpha \beta }=\frac{8}{7}\] \[\Rightarrow \frac{(16/5)}{2\,(8/7)}=\alpha \beta \] \[\Rightarrow \,\,\alpha \beta =\frac{7}{5}\] ?..(ii) \ Equation is \[{{x}^{2}}-\left( \frac{16}{5} \right)x+\frac{7}{5}=0\] \[\Rightarrow \,\,5{{x}^{2}}-16x+7=0\].
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