Question

If $P\left(x\right)$ is a polynomial of degree less than or equal to $2$ and $S$ is the set of all such polynomials so that $P\left(1\right)=1,P\left(0\right)=0$ and $P^{\prime }\left(x\right)>0$ $\forall$ $x\in [0,1]$, then

• A. $S=\varphi$
• B. $S=(1-a)x^2+ax$ for $0<a<2$
• C. $(1-a)$ $x^2+ax$ for $a\in (O,\infty )$
• D. $S=\left\{\right(1-a)x^2+ax$ for $0<a<1$

Answer 1

The correct option is B $S=(1-a)x^2+ax$ for $0<a<2$