How to determine the number of solutions

vastsky

Given a function in the form of: a0+a1*sqrt(2)*cos(pi*x)+a2*sqrt(2)*cos(2*pi*x)+a3*sqrt(2)*cos(3*pi*x)+. ..., where a0, a1, a2,... are known constant coefficients, sqrt(2) is the square root of 2, pi is 3.14159..., and the number of coefficients are predetermined. In addition, x is defined in (0,1). Is there a way to quickly determine how many solutions this function has? In other words, how many times it intersects with the x-axis? Thanks in advance!!