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**1. The problem statement, all variables and given/known data**

Find the basis and dimension of the following subspace U of P

_{2}

p(x) [tex]\ni[/tex] P

_{2}such that p(1) = p(2)

**2. Relevant equations**

**3. The attempt at a solution**

I know all quadratics are in the form ax

^{2}+ bx + c

set p(2) = p(1)

4a + 2b + c = a + b + c

b = -3a

Therefore ax

^{2}-3a + c

Basis(U) = a(x

^{2}-3x) + c

Therefore dim(U) = 2

I'm just wondering if I have the correct answer or not. Going into linear algebra midterm tomorrow and prof never really went over polynomials but it's on the test.