Find the dimension of each b The space of cubic polynomials

Find the dimension of each.

(b) The space of cubic polynomials p(x) such that p(7) = 0 and p(5) = 0

Solution

b) Given that cubic polynomial p(x).

p(7) = 0 and p(5) = 0

Then,

p(x) = (x-5) (x-7) (a+bx)

p1(x) = (x-5) (x-7) , p2(x) = x (x-5) (x-7) forms the basis.

Therefore,

dimension of the space = 2