If the roots of the equation x3 – ax2 + bx – c = 0 are three conse

1.	If the roots of the equation x3 – ax2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ?(a) \(-\frac{1}{\sqrt3}\)(b) –1 (c) 0 (d) 1
Answer» (b) -1 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.

If the roots of the equation x3 – ax2 + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b ?(a) \(-\frac{1}{\sqrt3}\)(b) –1 (c) 0 (d) 1

Answer»

(b) -1

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.