A) \[{{x}^{2}}-16x-25=0\]
B) \[{{x}^{2}}-8x+5=0\]
C) \[{{x}^{2}}-16x+25=0\]
D) \[{{x}^{2}}+16x-25=0\]
Correct Answer: C
Solution :
Given that \[A.M.=8\] and \[G.M.=5\], if \[\alpha ,\ \beta \] are roots of quadratic equation, then quadratic equation is \[{{x}^{2}}-x(\alpha +\beta )+\alpha \beta =0\] ......(i) \[A.M.=\frac{\alpha +\beta }{2}=8\]\[\Rightarrow \]\[\alpha +\beta =16\] ......(ii) and \[G.M.=\sqrt{\alpha \beta }=5\]\[\Rightarrow \]\[\alpha \beta =25\] ......(iii) So the required quadratic equation will be \[{{x}^{2}}-16x+25=0\].
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