Question

The number of cubic polynomials $P\left(x\right)$ satisfying $P\left(1\right)=2,P\left(2\right)=4,P\left(3\right)=6,P\left(4\right)=8$ is

• A. $0$
• B. $1$
• C. more than one but finitely many
• D. infinitely many

Answer 1

The correct option is A $0$

Let $f\left(x\right)=2x.$
Now according to the question, $f\left(x\right)$ and $P\left(x\right)$ intersect at four points ($x=1,x=2,x=3,x=4$), which is not possible.
So, no such cubic polynomial exists.