• # question_answer If the A.M. and G.M. of roots of a quadratic equations are 8 and 5 respectively, then the quadratic equation will be [Pb. CET 1990] A) ${{x}^{2}}-16x-25=0$ B) ${{x}^{2}}-8x+5=0$ C) ${{x}^{2}}-16x+25=0$ D) ${{x}^{2}}+16x-25=0$

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 ${{x}^{2}}-16x+25=0$.