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Question
Construct a cubic equation with roots `2, 1/2, and 1`
Solution
α = 2, β = `1/2`, γ = 1
α + β + γ = `2 + 1/2 + 1`
= `(4 + 1 + 2)/2`
= `7/2`
αβ + βγ + γα = `2 xx 1/2 + 1/2 xx 1 + 2 xx 1`
= `1 + 1/2 + 2`
= `7/2`
αβγ = `2 xx 1/2 xx 1` = 1
`x^3 - 7/2 x^2 + 7/2 x - 1` = 0
Multiplying by 2
2x3 – 7x2 + 7x – 2 = 0
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