When determining intercepts algebraically what does it mean if you get an imaginary solution?

When determining intercepts algebraically and you get an imaginary solution, this would mean that the graph of the function does not pass through the x or the y axis. X-intercept is the value of x when y would be equal is zero or the value x when the graph passes / intersects the x-axis. On the other hand, the y-intercept is the value of y when x is zero or the value of y when the plot intersects the y-axis. Therefore, the value of these intercepts should be real values and not imaginary numbers or else these intercepts do not exist. The plot of the equation would not cross any of the axes in the coordinate.