Find the polynomial with zeros alpha & beta where alpha-beta=2 and alpha.beta=15
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α-β=2 and αβ = 15
(α+β)^2 = (α-β)^2 + 4αβ
(α+β)^2 = (2)^2 + 4(15)
(α+β)^2 = 64
(α+β) = +8 or -8
The polynomial is
x² - (α+β)x + αβ
x² - 8x + 15 or x² +8x + 15
(α+β)^2 = (α-β)^2 + 4αβ
(α+β)^2 = (2)^2 + 4(15)
(α+β)^2 = 64
(α+β) = +8 or -8
The polynomial is
x² - (α+β)x + αβ
x² - 8x + 15 or x² +8x + 15
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