2.1 Nature of the roots of a quadratic equation

2.1 Nature of the roots of a quadratic equation

On solving quadratic equations, we get different kinds of roots. Now we will discuss the nature or characteristics of the roots of the quadratic equation without actually solving it.

2.1.1 Discriminant $(b^{2} - 4ac)$ of the quadratic expression $ax^{2} + bx + c$

We know that two roots of the equation $ax^{2} + bx + c = 0$ , $a \neq 0$ (i)

The nature of these roots depends on the value of the expression $b^{2} - 4ac$ which is called the "discriminant" of the quadratic equation (i) or the quadratic expression $ax^{2} + bx + c$ .

2.1.2 To find the discriminant of a given quadratic equation.

We explain the procedure to find the discriminant of a given quadratic equation through the following example: