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Verified answer
3x²-x-4 = 0x1+x2 = ⅓
x1.x2 = -4/3
α = 3x1-1
β = 3x2-1
α+β = (3x1-1)+(3x2-1)
= 3(x1+x2) - 2
= 3 (⅓) - 2
= 1
α.β = (3x1-1)(3x2-1)
= 9x1.x2 -3 (x1+x2) +
= 9(-4/3) - 3(⅓) + 1
= -12 -1+1
= -12
pk : x² - (α+β)x + αβ = 0
: x² - x - 12 = 0