. . Quadratic Equations For the quadratic equation ax bx + = , b ac is called the discriminant and it is usually denoted by D . We know that −+ ∆ and −− ∆ are roots of the ax bx .
The two roots together are usually written as −± ac . It is unnecessary to emphasize that a ¹ , since by saying that ax bx + + is a quadratic polynomial, it is implied that a ¹ . We also learnt that ∆= if, and only if, the roots are equal. When a b c , , are real, we know • ∆> 0if, and only if, the roots are real and distinct • ∆< if, and only if, the quadratic equation has no real roots.