Two polynomials $f$ and $g$ are orthogonal, when the dot-product $\langle f,g \rangle = 0$.
How can I describe all polynomials $f$ and $g$, each with a degree of $1$, that are orthogonal to each other?
I've found the example $f(x) = -3x + 1$ and $g(x) = x + 1$, but I cannot find a good generalization for $f$ and $g$.
I'd love to hear some ideas! :)