Quadratic Equation Calculator From Roots
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Reviewed by Calculator Editorial Team
This quadratic equation calculator helps you find the standard form of 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 solution.
Introduction
A quadratic equation is a second-degree polynomial equation in a single variable. The general form is:
When you know the roots (solutions) of the equation, you can find the quadratic equation that produced those roots. This is useful in various mathematical and scientific applications.
Formula
If a quadratic equation has roots r₁ and r₂, the standard form of the equation can be written as:
This formula is derived from the factored form of a quadratic equation:
Expanding this factored form gives the standard quadratic equation.
How to Use the Calculator
- Enter the first root (r₁) in the first input field.
- Enter the second root (r₂) in the second input field.
- Click the "Calculate" button to see the quadratic equation.
- The result will display the standard form of the quadratic equation.
- Use the "Reset" button to clear the inputs and results.
Note: The calculator assumes the coefficient of x² is 1. If you need a different coefficient, you can multiply the entire equation by that value.
Worked Example
Let's find the quadratic equation with roots 3 and -2.
- Sum of roots: 3 + (-2) = 1
- Product of roots: 3 × (-2) = -6
- Using the formula: x² - (1)x + (-6) = 0 → x² - x - 6 = 0
The quadratic equation is x² - x - 6 = 0.
FAQ
- 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.
- How do I find the roots of a quadratic equation?
- You can find the roots using the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a).
- Can the calculator handle complex roots?
- Yes, the calculator can handle complex roots. Simply enter the complex numbers in the format a+bi or a-bi.
- What if I have a repeated root?
- If you have a repeated root (r), the quadratic equation will be (x - r)² = 0, which expands to x² - 2rx + r² = 0.
- Is the calculator free to use?
- Yes, the quadratic equation calculator is completely free to use with no restrictions.