If the roots of the equation x^3 – ax^2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ? -Maths 9th

If the roots of the equation x^3 – ax^2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ? -Maths 9th
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Let the roots of the equation x3 – ax2 + bx – c = 0 be  (α – 1), α, (α + 1)  ∴ S2 = (α – 1)α + α(α + 1) + (α + 1) (α – 1) = b  ⇒ α2 – α + α2 + α + α2 – 1 = b ⇒ 3α2 – 1 = b ∴ Minimum value of b = – 1, when α = 0.
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