Examples Using Discriminant FormulasĮxample 1: Determine the discriminant of the quadratic equation 5x 2 + 3x + 2 = 0. We can see the applications of the discriminant formulas in the following section. Learn the why behind math with our certified experts If D If D = 0, then all the three roots are real where at least two of them are equal to each other.If D 0, all the three roots are real and distinct.
If D = 0, then the quadratic formula becomes x = / and hence in this case the quadratic equation has only one real root. Here D can be either > 0, = 0, (or) 0, then the quadratic formula becomes x = / and hence in this case the quadratic equation has two distinct real roots. Thus, the quadratic formula becomes x = /. Here, b 2 - 4ac is the discriminant D and it is inside the square root. According to the quadratic formula, the roots can be found using x = /. We know that a quadratic equation has a maximum of 2 roots as its degree is 2. We know that the quadratic formula is used to find the roots of a quadratic equation ax 2 + bx + c = 0. The discriminant formula of a quadratic equation ax 2 + bx + c = 0 is, Δ (or) D = b 2 - 4ac. The discriminant formulas for a quadratic equation and cubic equation are:ĭiscriminant Formula of a Quadratic Equation The discriminant of a quadratic equation is derived from the quadratic formula. The discriminant formulas give us an overview of the nature of the roots. 
Let us learn the discriminant formulas along with a few solved examples. The discriminant of a polynomial is a function that is made up of the coefficients of the polynomial.
Especially, the discriminant of a quadratic equation is used to determine the number and the nature of the roots. The discriminant formulas are used to find the discriminant of a polynomial equation.
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