Vector spaces of polynomials
Algebra
Level
pending
Which of the following sets of polynomials are vector spaces over \(\mathbb{R}\) with the usual polynomial addition and scalar multiplication?
\(A\): All polynomials of the form \(p(x)=ax^2 + bx + c\) with \(a,b,c\in\mathbb{R}\) and \(a+b+c=1\).
\(B\): All polynomials of the form \(p(x) = ax^2 + bx + c\) with \(a,b,c\in\mathbb{R}\) and \(a+b+c=0\).
\(C\): All polynomials of the form \(p(x)=ax^2 + bx + c\) with \(a,b,c\in\mathbb{R}\) and \(p(1) = p(2)\).
by
Ognjen Vukadin