Last updated at Sept. 3, 2021 by Teachoo
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Ex 9.3, 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
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