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## Homework Statement

Find a basis for the set of polynomials in P3 with P'(1)=0 and P''(2)=0.

## Homework Equations

P' is the first derivative, P'' is the second derivative.

## The Attempt at a Solution

The general form of a polynomial in P3 is ax^3+bx^2+cx+d

Therefore, P' will have the form 3ax^2+2bx+c

and P'' will have the form 6ax + 2b

Plugging in the known values, the two equations will be:

3a+2b+c=0

12a+2b+0c=0

I just don't know where to go from there, how to find the basis. I understand the concept of a basis and how to find one for a set of matrices or vectors, but not with this. Any help would be greatly appreciated. Thank you.