# Thread: leading coefficient

1. ## leading coefficient

given that { f(x), f' (x)..., f^n (x)} is a basis for Pn,

then a_0 f(x)+ a_1 f'(x)+...a_n f^n (x)=0 , hw can you tell that the leading coefficient is a_0 a_n and that

for a_1 f'(x)+...a_n f^n (x)=0 where a_0 f(x)=0 then the leading coefficient is 2a_1 a_n?

2. I'm not sure what you mean by leading coefficient; leading coefficient of what?

Since the set $\left\{ f,f^\prime ,\ldots ,f^{(n)}\right\}$ is a basis for $\mathbb{P}_n$, the first equation you have implies each $a_i$ is 0.