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Question
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
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Solution
P(s) = 4s2 – 4s + 1
4s2 – 2s – 2s + 1 = 0
2s(2s – 1) – 1(2s – 1) = 0
(2s – 1) (2s – 1) = 0
s = `1/2`, s = `1/2`
a = 4, b = – 4, c = 1, ∝ = `1/2`, β = `1/2`
∝ + β = `(-b)/a`, ∝β = `c/a`
`1/2 + 1/2 = (-4)/4, (1/2)(1/2) = 1/4`
`(1 + 1)/2 = (+4)/4, 1/4 = 1/4`
`2/2` = 1
1 = 1
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