Quadratic From Roots Calculator

This calculator helps you find the quadratic equation when you know its roots. Whether you're a student studying algebra or a professional working with quadratic equations, this tool provides a quick and accurate solution.

What is Quadratic from Roots?

A quadratic equation is a second-degree polynomial equation in a single variable. It has the general form:

General Form of Quadratic Equation

ax² + bx + c = 0

The roots of a quadratic equation are the values of x that satisfy the equation. If you know the roots of a quadratic equation, you can find the equation itself using the roots.

How to Find Quadratic Equation from Roots

To find the quadratic equation from its roots, you can use the following steps:

Identify the roots of the quadratic equation.
Use the formula to find the coefficients a, b, and c.
Write the quadratic equation in the standard form.

This process is useful in various mathematical and scientific applications where you need to derive the equation from known solutions.

Formula

If a quadratic equation has roots r₁ and r₂, the equation can be written as:

Quadratic Equation from Roots

(x - r₁)(x - r₂) = 0

Expanding this equation gives the standard form of the quadratic equation:

Expanded Form

x² - (r₁ + r₂)x + (r₁ × r₂) = 0

This formula allows you to find the quadratic equation when you know its roots.

Example

Let's find the quadratic equation with roots 3 and 5.

Identify the roots: r₁ = 3, r₂ = 5.
Use the formula: (x - 3)(x - 5) = 0.
Expand the equation: x² - (3 + 5)x + (3 × 5) = 0 → x² - 8x + 15 = 0.

The quadratic equation with roots 3 and 5 is x² - 8x + 15 = 0.

FAQ

What is the difference between a quadratic equation and a linear equation?

A quadratic equation has a highest degree of 2, while a linear equation has a highest degree of 1. Quadratic equations have a parabolic graph, while linear equations have a straight line graph.

How do I find the roots of a quadratic equation?

You can find the roots of a quadratic equation using the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a). Alternatively, you can factor the equation if it can be easily factored.

What is the significance of the roots of a quadratic equation?

The roots of a quadratic equation represent the x-intercepts of the parabola defined by the equation. They are the points where the graph crosses the x-axis.