If S is a set of $$P(x)$$ is polynomial of degree ≤$$2$$ such that $$P(0)=0$$, $$P(1)=1$$, P'(x)>$$0$$ ∀x∈(0$$,$$1), then

Correct option is 4S=ax+(1-a)x2∀a∈(0,2)

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If S is a set of $P (x)$ is polynomial of degree $\leq 2$ such that $P (0) = 0, P (1) = 1, P^{'} (x) > 0 \forall x \in (0, 1),$ then

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S=0

S=ax+(1-a)x2∀a∈(0,∞)

S=ax+(1-a)x2∀a∈R

S=ax+(1-a)x2∀a∈(0,2)

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detailed solution

Correct option is D

Let P(x)=bx2+ax+cAs P(0)=0⇒c=0As P(1)=1⇒a+b=1P(x)=ax+(1-a)x2Now P'(x)=a+2(1-a)xas P'(x)>0 for x∈(0,1)Only option (4) satisfies above condition

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If S is a set of P(x) is polynomial of degree ≤2 such that P(0)=0, P(1)=1, P'(x)>0 ∀x∈(0,1), then

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If S is a set of $P (x)$ is polynomial of degree $\leq 2$ such that $P (0) = 0, P (1) = 1, P^{'} (x) > 0 \forall x \in (0, 1),$ then