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

Last updated at April 16, 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)

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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