Question

How to use the discriminant to find out what type of solutions the equation has for `qx^2+rx+s=0`?

Answer 1

The discriminant of `qx^2+rx+s=0` is given by the formula:

`Delta = r^2-4qs`

If `Delta < 0` then the quadratic equation has no real solutions. It has two distinct complex roots (complex conjugates of one another).

If `Delta = 0` then the quadratic equation has one repeated root. If `q`, `r` and `s` are rational then the repeated root is rational too.

If `Delta > 0` then the quadratic equation has two distinct real roots. If `q`, `r` and `s` are rational and `Delta` is the square of a rational number, then the roots will be rational too.