Determine the type of triangle constructed on the polynomials

Question

Determine the type of triangle constructed on the polynomials:
2-t+5t² , 3t²+2t+1 ,

if the scalar product is defined as follows:

(f,g) = a₀b₀ + 2a₁b₁ + 3a₂b₂

I just don't understand what 'triangle constructed on the polynomials' means

Answer 1

One interpretation of the regular scalar product $(a,b)$ is the length of the projection of vector $a$ onto vector $b$, or vice-versa. If you draw the two vectors, and a line joining the tip of $a$ to a point on $b$ which is $(a,b)$ from the tail (the tip of the projection of $a$ on $b$), you get a right-angled triangle. By changing the definition of the scalar product, and repeating the drawing process, you could get a different triangle; e.g. acute or obtuse.

Maybe this is what the question is asking. Though I don't know how thew polynomials are involved.