AM and GM (Arithmetic Mean And Geometric mean)
AM and GM (Arithmetic Mean And Geometric mean)
Last updated at April 16, 2024 by Teachoo
Ex 8.2, 32 If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation. Introduction If 2,3 are the roots or a quadratic equation, The quadratic equation is x2 β (2 + 3) x + (2 Γ 3) = 0 x2 β 5x + 6 = 0 Therefore, If πΌ & π½ be the root of the quadratic equation So, the quadratic equation becomes x2 β (Sum of roots)x + (product of roots) = 0 i.e. x2 β (πΌ + π½)x + πΌπ½ = 0 Ex9.3, 32 If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation. Let πΌ & π½ be the root of the quadratic equation It is given that AM of roots is 8 AM of πΌ & π½ = 8 (πΌ + π½)/2 = 8 πΌ + π½ = 16 Thus, πΌ + π½ = 16 & πΌπ½ = 25 Now, our quadric equation is x2 β (Sum of roots)x + (Product of roots) = 0 x2 β (πΌ + π½)x + (πΌπ½) = 0 Putting πΌ + π½ = 16 , πΌπ½ = 25 from (1) & (2) x2 β 16x + 25 = 0 Thus, the required quadratic equation is x2 β 16x + 25 = 0