Orthogonal wrt to linear polynomial(s)

[jegues]

Homework Statement

See figure attached for problem statement as well as my attempt.

Homework Equations

The Attempt at a Solution

I can't see how we are expected to solve for 2 unknowns with only one equation? What am I missing? Am I supposed to simply define a in terms of b?

Thanks again!

 

[Kreizhn]

Assuming that your math is correct, then you're done. If you had two equations and two unknowns there would only be one value of (a,b) that would work. If you have two unknowns in one equation, then you have a one-parameter family of solutions, all of which work. In fact, you would hope there would be a family of solutions, since if w(x) ensures that f and g are orthogonal, then any scalar multiple of w(x) should also make f,g orthogonal right?

 

[jegues]

Assuming that your math is correct, then you're done. If you had two equations and two unknowns there would only be one value of (a,b) that would work. If you have two unknowns in one equation, then you have a one-parameter family of solutions, all of which work. In fact, you would hope there would be a family of solutions, since if w(x) ensures that f and g are orthogonal, then any scalar multiple of w(x) should also make f,g orthogonal right?

So aside for any algebra mistake that may or may not have occurred in the process, I seem to have the right idea?