Question

The value of ‘a’ for which the equation x³ – 3x + a = 0 has two different roots in [0, 1] is given by –

• A. –1
• B. 2
• C. 1
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Let α, β be two different roots of ƒ(x) = 0 in [0, 1] where ƒ(x) = x³ – 3x + a. Therefore, by Rolle’s theorem ƒ ′ (x) = 0 has a root between α and β, i.e. in (0, 1). But, ƒ ′ (x) = 0

⇒ 3x² – 3 = 0 ⇒ x = ±1

∴ ƒ ′ (x) = 0 has no roots in (0, 1)

Hence the given equation has no root lying between 0 and 1 for any value of a.