Write Quadratic Equation Root Calculator

This calculator helps you write a quadratic equation in standard form when you know its roots. Whether you're a student studying algebra or a professional working with quadratic functions, understanding how to construct a quadratic equation from its roots is essential.

How to Use This Calculator

Using the quadratic equation root calculator is simple:

Enter the first root of the quadratic equation in the "First Root" field.
Enter the second root of the quadratic equation in the "Second Root" field.
Click the "Calculate" button to generate the quadratic equation.
The calculator will display the standard form of the quadratic equation based on the roots you provided.

You can also use the "Reset" button to clear all inputs and start over.

The Formula

A quadratic equation in standard form is written as:

ax² + bx + c = 0

When you know the roots of the equation, you can write the equation in its factored form:

a(x - r₁)(x - r₂) = 0

Where r₁ and r₂ are the roots of the equation. To convert this to standard form, you expand the factored equation.

Worked Example

Let's say you have a quadratic equation with roots at x = 3 and x = -2. Here's how you would write the equation in standard form:

Start with the factored form: (x - 3)(x - 2) = 0
Expand the equation: x² - 2x - 3x + 6 = 0
Combine like terms: x² - 5x + 6 = 0

So, the standard form of the quadratic equation with roots at x = 3 and x = -2 is x² - 5x + 6 = 0.

FAQ

What is a quadratic equation?: A quadratic equation is a second-degree polynomial equation in a single variable x, with at least one x² term. It has the general form ax² + bx + c = 0.
What are the roots of a quadratic equation?: The roots of a quadratic equation are the values of x that satisfy the equation. They are also known as the solutions or zeros of the equation.
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).
Can I write a quadratic equation with complex roots?: Yes, you can write a quadratic equation with complex roots. The roots will be complex conjugates, and the equation will have real coefficients.
What if I only know one root of the quadratic equation?: If you only know one root, you can use the sum and product of the roots to find the other root. The sum of the roots is -b/a, and the product of the roots is c/a.