### 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. $-2{x}^{2}+5x-9=0$

**Answer**