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Question 27 - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at July 26, 2023 by

 

If α,β are zeroes of quadratic polynomial 5x^2+5x+1, find  the value of

1. α^2+β^2

2. α^(-1)+β^(-1)

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Transcript

Since 𝛼 and 𝛽 are roots of 5π‘₯^2+5π‘₯+1 Sum of zeroes 𝛼 + 𝛽 = (βˆ’ (5))/5 𝜢 + 𝜷 = βˆ’1 Product of zeroes 𝛼𝛽= 1/5 𝜢𝜷 = 𝟏/πŸ“ Finding 𝜢^𝟐+𝜷^𝟐 Since γ€–(𝛼" + " 𝛽)γ€—^2 = 𝛼^2+𝛽^2 + 2𝛼𝛽 𝜢^𝟐+𝜷^𝟐 = γ€–(𝜢" + " 𝜷)γ€—^𝟐 βˆ’ 𝟐𝜢𝜷 Substituting values from (1) and (2) γ€– 𝛼〗^2+ 𝛽^2 = γ€–(βˆ’1)γ€—^2 βˆ’ 2 Γ— 1/5 γ€– 𝛼〗^2+ 𝛽^2 = 1 βˆ’ 2/5 γ€– 𝛼〗^2+ 𝛽^2 = (5 βˆ’ 2)/5 𝜢^𝟐+𝜷^𝟐 = πŸ‘/πŸ“ Finding 𝜢^(βˆ’πŸ)+𝜷^(βˆ’πŸ) 𝛼^(βˆ’1)+𝛽^(βˆ’1) = 𝟏/𝜢 + 𝟏/𝜷 = (𝜷 + 𝜢)/𝜢𝜷 = (βˆ’1)/(1/5) = -1 Γ— 5/1 = βˆ’5

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.