# Discriminant of a Quadratic Equation

### The Discriminant

The expression $${{b^2} - 4ac}$$ in the general formula is called the discriminant of the equation, as it determines the type of roots that the equation has.

Example
Determine the nature of the roots of the following equations.
a. $$5{x^2} - 7x + 3 = 0$$
b. $${x^2} - 4x + 4 = 0$$
c. $$- 2{x^2} + 5x - 9 = 0$$