Roots of Quadratic Equation
The Roots of Quadratic equation are the two values of x, which are calculated from the quadratic equation. Values of xo which satisfies the quadratic equation q(x) are called the roots of the quadratic equation. This implies that for any xo if q(x) = 0. Then xo is the root of the q(x).
For example, the roots of the quadratic equation q(x): 3x2 – 10x – 8 = 0 are x = -2/3 and x = 4.
For x = -2/3,
q(-2/3) = 3(-2/3)2 – 10(-2/3) – 8
⇒ q(-2/3) = 4/3 + 20/3 – 8
⇒ q(-2/3) = 0
Note: Quadratic equation is a two degrees polynomial i.e., it can have a maximum of 2 roots.
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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
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