I am having problem with this question

T: P2 --->R^2 T(a+bx+cx^2)=(a,b)

Find the basis for the kernel T and basis for the image T

according to the text book Kernel = { T(v)= 0 }, so the kernel should look like

T (a+bx+cx^2)=(0,0)

how exactly do you find the basis?

As for the image, up to my understanding, is it the entire vector space of P2 map into a subspace of R^2?