Find Range of V0 for Particle in Potential

[peripatein]

Homework Statement

A particle is in the following potential:
V(x)=infinity for x<0; -V₀ for 0<x<a; and 0 for x>a
Given that there's only one bound state I am asked to determine the range of values for V₀ in terms of the width a and the particle's mass m.[/B]

Homework Equations

The Attempt at a Solution

For -V₀<E<0 I chose the following general solution for the wave function:
ψ(x)=Asin(kx) 0<x<a; Bexp(-qx) x>0
where k=√(2m(E+V₀)/ħ and q=√(2m|E|)/ħ
By demanding continuity at x=a for both wave functions and their derivatives I obtained the following solution:
q=-kctg(ka)
How may I proceed? I'd appreciate some guidance.
[/B]

 

[mfb]

How do you get the number of solutions from your last equation?
The borders for "a" and "m" are exactly the limiting cases for 1 and 2 solutions.