Keeping in mind that the quadratic equation has complex zeros, how many x-intercepts does the graph have?

A quadratic equation has exactly 2 roots (Real and non-real, which we often describe as complex).

If one of the zeros of a quadratic is complex, the second is the conjugate of the first root, so it is also complex. Thus, we complete our 2 roots, meaning that there can't be any other, real root.

Having no real root means that the parabola (the graph of the quadratic) does no intersect the x-axis - that is, it is entirely above the x-axis, or entirely below it.

Answer: No x-intercepts.

Remark: Real numbers are included in Complex numbers, so a "complex zero" could be a "real zero", and all real zeros are complex zeros. All complex numbers a+bi with b=0 are real. But often, as it appears to be the case here, "complex" is used as a substitute for non-real.