The coefficients of a quadratic are real. If the zeroes are complex, there must be two of them so that the imaginary components cancel out. They will be complements of one another, e.g., 1+i and 1-i, or, generally, a+ib and a-ib, where a and b are real. Their sum is 2a and their product is a^2+b^2, both of which are real. If only one zero was complex or imaginary, it would make the coefficients of the quadratic imaginary or complex.