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Question
If α, β are zeroes of quadratic polynomial 5x2 + 5x + 1, find the value of α2 + β2.
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Solution
P(x) = 5x2 + 5x + 1
α + β = `(-b)/a = (-5)/5` = – 1
αβ = `c/a = 1/5`
α2 + β2 = (α + β)2 – 2αβ
= `(-1)^2 - 2(1/5)`
= `1 - 2/5`
= `3/5`
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