Write Quadratic Equation Given Roots Calculator

This calculator helps you write a quadratic equation when you know its roots. Whether you're a student studying algebra or a professional working with quadratic functions, this tool provides a quick and accurate way to construct the equation from its roots.

How to Use This Calculator

Using the quadratic equation 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.
Review the result and use it as needed.

The calculator will display the standard form of the quadratic equation based on the roots you provide.

The Formula Explained

A quadratic equation can be written in its standard form as:

ax² + bx + c = 0

When you know the roots of the equation (let's call them r₁ and r₂), you can write the equation in its factored form:

a(x - r₁)(x - r₂) = 0

To convert this to standard form, you expand the factored equation:

ax² - a(r₁ + r₂)x + a(r₁r₂) = 0

This is the formula used by this calculator to generate the quadratic equation from its roots.

Worked Example

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

Enter 3 in the "First Root" field.
Enter -2 in the "Second Root" field.
Click "Calculate".

The calculator will generate the quadratic equation:

x² + x - 6 = 0

This is because:

(x - 3)(x + 2) = x² - x - 6 = 0

Notice that the coefficient 'a' is 1 in this case. If you want a different leading coefficient, you can multiply the entire equation by that value.

Frequently Asked Questions

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.

How do I find the roots of a quadratic equation?

The roots of a quadratic equation can be found using the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a).

Can I use this calculator for complex roots?

Yes, this calculator can handle complex roots. The resulting equation will reflect the complex nature of the roots.