Obtaining Polynomials: Probability & Ways

[haya]

In how many ways can obtain polynomial from
[PLAIN]http://im3.gulfup.com/2011-05-05/1304543619801.gif

notes that c any coffieceints is in{0.1}
also in how many ways can obtain even ploynomials?whats the probability that we can obtain P(1,1,1)=0

 

[matiasmorant]

there infinitely many polynomials of that form; since there are infinitely many possibilities for choosing a single coefficient between 0 and 1. and you have to choose a bunch of them.
in an even polynomial, the coefficients of odd powers are 0, still you would have bunch of coefficients which don't need to be 0 and can be chosen at random. by the same argument as above, there are infinitely many even polynomials of that form.
if x=y=z=1, then the equation would be just a sum of a number of random numbers, all between 0 and 1. there are infinitely many possible combnations; but the only one which will give 0, is that all of the coeffcients are 0. so, the probability that P(1,1,1)=0 is
1/infinity=0.
after writing the answer I realized that maybe you don't mean the interval between 0 and 1 but only 0 and 1, was that your question?