Shouldn't you also assume that the quadratic is one of the factors of an arbitrary polynomial?
I guess soShouldn't you also assume that the quadratic is one of the factors of an arbitrary polynomial?
What do you mean by "both equations are equal"?
Well I found the equations that satisfied each root separately and they happened to be equal and thus have the equation has both roots given.What do you mean by "both equations are equal"?
How does this allow us to prove that P(p + sqrt(q)) = 0 -> P(p - sqrt(q)) = 0? (for any integer polynomials P)
Your argument needs to be clearer for it to be a mathematical proofWell I found the equations that satisfied each root separately and they happened to be equal and thus have the equation has both roots given.
Your argument needs to be clearer for it to be a mathematical proof
I'm still not sure what you are trying to say here, the equations and both have a root in common, but why does tha tell us anything special about those equations?
Right, then the next step is to show that any integer polynomial P has to have the same property
This question requires clarification before I can work on it.
This question requires clarification before I can work on it.
magnitude of force? speed of ball? I'm not sure how to work with a dimensionless vector.
I think it essentially can have any speed and the answer is not impacted, because the path traced out is the same (I think we are assuming a perfect mathematical universe with no friction or loss of energy in any way, and perfect reflection off the walls; so the ball moves for an infinite amount of time (and the speed is constant)).magnitude of force? speed of ball? I'm not sure how to work with a dimensionless vector.
This does not match the answer I got for the special case theta = pi/4I got cos(theta) over 2
I am flummoxed. Solutions?