QJEEAdv05Mac1e0: JEE Advanced 2005 Mathematics - Class 12 JEEAdv05Mac1e0 Solution: If is a polynomial of degree less than or equal to and is the…

Question

Verified Solution • 2025–26 Session moderate

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'\left( x \right) &gt; 0\,\,\forall x \in \left[ {0,1} \right],

then

A $S = \phi$
B $S = ax + \left( {1 - a} \right){x^2}\,\,\forall \,a \in \left( {0,2} \right)$
C $S = ax + \left( {1 - a} \right){x^2}\,\,\forall \,a \in \left( {0,\infty } \right)$
D $S = ax + \left( {1 - a} \right){x^2}\,\,\forall \,a \in \left( {0,1} \right)$

Accepted Answer

Answer

No answer available for this question.