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Question
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α–1 + β–1.
Solution
P(x) = 5x2 + 5x + 1
α + β = `(-b)/a = (-5)/5` = – 1
αβ = `c/a = 1/5`
α–1 + β–1 = `1/α + 1/β`
= `((α + β))/(αβ)`
= `((-1))/(1/5)`
= – 5
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