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)
CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard
Last updated at April 16, 2024 by Teachoo
Since πΌ and π½ are roots of 5π₯^2+5π₯+1 Sum of zeroes πΌ + π½ = (β (5))/5 πΆ + π· = β1 Product of zeroes πΌπ½= 1/5 πΆπ· = π/π Finding πΆ^π+π·^π Since γ(πΌ" + " π½)γ^2 = πΌ^2+π½^2 + 2πΌπ½ πΆ^π+π·^π = γ(πΆ" + " π·)γ^π β ππΆπ· Substituting values from (1) and (2) γ πΌγ^2+ π½^2 = γ(β1)γ^2 β 2 Γ 1/5 γ πΌγ^2+ π½^2 = 1 β 2/5 γ πΌγ^2+ π½^2 = (5 β 2)/5 πΆ^π+π·^π = π/π Finding πΆ^(βπ)+π·^(βπ) πΌ^(β1)+π½^(β1) = π/πΆ + π/π· = (π· + πΆ)/πΆπ· = (β1)/(1/5) = -1 Γ 5/1 = β5