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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

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.