Let α & β be the roots of a quadratic equation such that A.M. & G.M.of α, β are 8 and 5 respectively.Since A.M. of the roots α and β = $\frac{\alpha+\beta}{2}$ ⇒ 8 = $\frac{\alpha+\beta}{2}$ ⇒ 16 = α + β ... (i) Since G.M. of the roots α and β = $\sqrt{\alpha\beta}$ ⇒ 5 = $\sqrt{\alpha\beta}$ ⇒ 25 = αβ ... (ii) As we know the general form of a quadratic equation, whose roots are α and β is $x^{2}$ – (α + β) x + ab = 0 ⇒ $x^{2}$ – 16x + 25 = 0 [from (i) & (ii)]