Use the formula or complete the square. The zeroes of the quadratic can be real and rational; real and irrational; complex conjugates. If the quadratic is ax²+bx+c, x=(-b+√b²-4ac)/2a. If b² > 4ac the solutions are real. If b²-4ac is a perfect square, the solutions are real and rational; otherwise they’re real but irrational. If b² < 4ac the solutions are complex.
