Select Quadratic Equation Given 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 functions, this tool provides a quick and accurate way to determine the equation from its solutions.

How to Use This Calculator

Using the quadratic equation given roots calculator is straightforward. Follow these steps:

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, which will display the standard form of the quadratic equation.

The calculator will also show you the step-by-step process of how the equation is derived from the given roots.

Formula Used

When you know the roots of a quadratic equation, you can construct the equation using the following formula:

If the roots are r₁ and r₂, the quadratic equation is:

x² - (r₁ + r₂)x + (r₁ × r₂) = 0

This formula is derived from the factored form of a quadratic equation, which is (x - r₁)(x - r₂) = 0. Expanding this expression gives you the standard form of the quadratic equation.

Worked Example

Let's say you have a quadratic equation with roots 3 and -2. Here's how you would find the equation using the calculator:

Example Calculation

Given roots: 3 and -2

Sum of roots: 3 + (-2) = 1

Product of roots: 3 × (-2) = -6

Quadratic equation: x² - (1)x + (-6) = 0 → x² - x - 6 = 0

Using the calculator, you would enter 3 in the first root field and -2 in the second root field. The calculator will then display the equation x² - x - 6 = 0.

Frequently Asked Questions

What is a quadratic equation?: A quadratic equation is a second-degree polynomial equation in a single variable, typically written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 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). Alternatively, you can use factoring or completing the square.
Can I use this calculator for complex roots?: Yes, this calculator can handle complex roots. Simply enter the complex numbers in the form a + bi or a - bi, where a and b are real numbers.
What if I only have one root?: If you only have one root, the quadratic equation will have a double root. In this case, the equation can be written as (x - r)² = 0, where r is the root.
Is this calculator accurate?: Yes, the calculator uses precise mathematical formulas to determine the quadratic equation from the given roots. The results are accurate as long as the inputs are correct.