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

Last updated at Dec. 13, 2024 by Teachoo

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 5𝑥^2+5𝑥+1 Sum of zeroes 𝛼 + 𝛽 = (− (5))/5 𝜶 + 𝜷 = −1 Product of zeroes 𝛼𝛽= 1/5 𝜶𝜷 = 𝟏/𝟓 Finding 𝜶^𝟐+𝜷^𝟐 Since 〖(𝛼" + " 𝛽)〗^2 = 𝛼^2+𝛽^2 + 2𝛼𝛽 𝜶^𝟐+𝜷^𝟐 = 〖(𝜶" + " 𝜷)〗^𝟐 − 𝟐𝜶𝜷 Substituting values from (1) and (2) 〖 𝛼〗^2+ 𝛽^2 = 〖(−1)〗^2 − 2 × 1/5 〖 𝛼〗^2+ 𝛽^2 = 1 − 2/5 〖 𝛼〗^2+ 𝛽^2 = (5 − 2)/5 𝜶^𝟐+𝜷^𝟐 = 𝟑/𝟓 Finding 𝜶^(−𝟏)+𝜷^(−𝟏) 𝛼^(−1)+𝛽^(−1) = 𝟏/𝜶 + 𝟏/𝜷 = (𝜷 + 𝜶)/𝜶𝜷 = (−1)/(1/5) = -1 × 5/1 = −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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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