Question 20514
The discriminant is the part of the quadratic formula under the radical.

The quadratic formula is: {{{x = (-b+-sqrt(b^2-4ac))/2a}}}

The discriminant is: {{{b^2-4ac}}}

The value of the discriminant can tell you something about the solutions to a quadratic equation, without actually solving the equation.

If the discriminant is positive, the quadratic equation has two real roots.
If the discriminant is negative, the quadratic equation has two complex (a+bi) roots.
If the discriminant is zero, the quadratic equation has one real root (a double root).

Applying this to your quadratic equation {{{x^2-2x-3=0}}}, the discriminant is: {{{(-2)^2-4(1)(-3)}}} = 16

The value of the discriminant is positive, therefore, the solution has two real roots.