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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 – (2 + 3) x + (2 Γ— 3) = 0 x2 – 5x + 6 = 0 Therefore, If 𝛼 & 𝛽 be the root of the quadratic equation So, the quadratic equation becomes x2 – (Sum of roots)x + (product of roots) = 0 i.e. x2 – (𝛼 + 𝛽)x + 𝛼𝛽 = 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 𝛼 & 𝛽 be the root of the quadratic equation It is given that AM of roots is 8 AM of 𝛼 & 𝛽 = 8 (𝛼 + 𝛽)/2 = 8 𝛼 + 𝛽 = 16 Thus, 𝛼 + 𝛽 = 16 & 𝛼𝛽 = 25 Now, our quadric equation is x2 – (Sum of roots)x + (Product of roots) = 0 x2 – (𝛼 + 𝛽)x + (𝛼𝛽) = 0 Putting 𝛼 + 𝛽 = 16 , 𝛼𝛽 = 25 from (1) & (2) x2 – 16x + 25 = 0 Thus, the required quadratic equation is x2 – 16x + 25 = 0

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.