If P ( x ) is a polynomial of degree less than or equal to 2 and S is the set of all such…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
If P(x) is a polynomial of degree less than or equal to 2 and S is the set of all such polynomials so that
P(0) = 0, P(1) = 1 and P′(x) > 0 ∀ x ∈ [0, 1], then
P(0) = 0, P(1) = 1 and P′(x) > 0 ∀ x ∈ [0, 1], then
- S = φ
- S = ax + (1 – a) x2 ∀a ∈ (0, 2)
- S = ax + (1 – a) x2 ∀a ∈(0, ∞)
- S = ax + (1 – a) x2 ∀a ∈ (0, 1)
Answer
(D) S = ax + (1 – a ) x 2 ∀ a ∈ (0, 1)
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