Nature of Roots
We can easily find the nature of roots of the quadratic equations without actually finding the roots. Generally, we represent the roots of quadratic equations with α and β symbols.
Discriminant
Discriminant provides important information about the nature and type of the roots of the equation. It is usually denoted as D or Δ.
Formula of discriminant of a quadratic equation is given by:
D = b2 – 4ac
Let’s understand the discriminant of a quadratic equation and the corresponding nature of its roots.
Discriminant and Nature of Roots |
||
---|---|---|
Discriminant (D) | Nature of Roots | Description |
D > 0 | Real and Distinct | The quadratic equation has two real and distinct roots. |
D = 0 | Real and Equal | The quadratic equation has two real and equal (coincident) roots. |
D < 0 | Complex or Imaginary | The quadratic equation has no real roots; instead, it has two complex or imaginary roots. |
Must Read
Quadratic Equations: Formula, Method and Examples
A Quadratic equation is a second-degree equation that can be represented as ax2 + bx + c = 0. In this equation, x is an unknown variable, a, b, and c are constants, and a is not equal to 0. To solve it, you can use methods such as factoring, completing the square, or the quadratic formula. Each method helps find the values of x that satisfy the equation.
Let’s learn how to solve Quadratic Equations using different methods in detail.
Table of Content
- What is Quadratic Equation?
- Quadratic Equation Standard Form
- Quadratic Equation Examples
- Roots of Quadratic Equation
- Quadratic Equations Formula
- Nature of Roots
- Discriminant
- Sum of Roots in Quadratic Equation
- Product of Roots in Quadratic Equation
- Writing Quadratic Equations using Roots
- How to Solve Quadratic Equation?
- Factorization Method
- Completing Square Method
- Graph Method
- Quadratic Equations Having Common Roots
- Maximum and Minimum Value of Quadratic Equation
- Quadratic Equation Sign Convention
- Solved Examples on Quadratic Equation
- Practice Questions on Quadratic Equation