What are the Roots of Quadratic Equation?

Nature of Roots of Quadratic Equation

In the context of quadratic equations, the term “roots” refers to the values of the variable (usually denoted as “x”) that satisfy the equation, making it true. We know that the standard representation of a Quadratic Equation is given as ax² + bx + c = 0. The roots of a quadratic equation are the values of “x” that, when substituted into the equation, make the equation true (i.e., equal to zero). There can be zero, one, or two real roots (values of “x”) depending on the discriminant (the value inside the square root) of the equation.

The roots of a Quadratic Equations is calculated using Quadratic Formula given below:

x = (-b ± √D)/2a

Where,

b is coffecicent of x,

D is Discriminant, and

a is coefficient of x².

In the above formula it is the Value of Discriminant that determines the nature of roots of a quadratic equation. The details of the Nature of Roots depending upon the value of discriminant of a quadratic equation has been discussed below.

Read more about Roots of Quadratic Equation.

Nature of Roots

Roots are the solutions of an equation. The Nature of Roots in mathematics refers to the characteristics and properties of solutions to algebraic equations. These roots represent the values that make the equation true. Understanding the nature of roots is essential for solving equations in science and engineering to analyzing data in statistics. Depending on the equation, roots can be real or complex, and their behavior can provide insights into mathematical relationships. Our context of root in this article is for Quadratic Equations. Nature of Roots is important for Class 10 students.

In this article, we will learn about what are the roots of a quadratic equation, how to determine the nature of roots of a quadratic equation specifying different cases, and solve examples based on the nature of roots.

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