Question

Is it possible to solve this problem?

1*g(0) + 1*g(1) + 3*g(-1) + 3*g(2) = 0


I know the function 0(x) would work, but, is there a way to find another polynomial with a degree of at most 3 that satisfies this equation?

Answer 1

I tried to make is so that it was 1 -1 3 -1

and I got a function g(x)=-2x+1. Is that a valid solution do you think? Is there a mathematical way to actually do this? I just guessed and checked, and got lucky! aha

Answer 2

I don't think I understand the problem.

Answer 3

I have this weird inner product space defined as

f*g = f(0)g(0) + f(1)g(1) + f(-1)g(-1) + f(2)g(2)

and I am given v=x^2 -x +1

I want to find a polynomial w, such that

v*w = 0 (the * as defined in f*g)

so, I found

f(0)=1
f(1)=1
f(-1)=3
f(2)=3

so, now my f*g becomes

1g(0) + 1g(1) +3g(-1) + 3g(2)= 0

I want to find this function g so that this holds true
...

(it turns out that g(x)=-2x +1 fits this definition. But this was just a lucky guess)

Answer 4

so, I am saying that w= -2x+1.

If this is confusing you, you're in the same boat. I'm pretty confused myself about it. I hope I am doing it correctly!