Root Calculator Given One Root

This root calculator helps you find the other root of a quadratic equation when you know one root. Whether you're solving math problems or analyzing data, this tool provides quick and accurate results with clear explanations.

Introduction

Quadratic equations are fundamental in algebra and appear in various real-world applications. When you know one root of a quadratic equation, you can find the other root using simple algebraic methods. This calculator simplifies the process by providing instant results and detailed explanations.

This calculator assumes you're working with a quadratic equation in the form ax² + bx + c = 0. If you have a different type of equation, you may need additional information to find the roots.

How to Use This Calculator

Enter the known root of your quadratic equation in the "Known Root" field.
Enter the coefficients of the quadratic equation in the "a", "b", and "c" fields.
Click the "Calculate" button to find the other root.
Review the result and the step-by-step solution provided.

Formula Explained

For a quadratic equation ax² + bx + c = 0 with known root r₁, the other root r₂ can be found using the following relationship:

Sum of Roots: r₁ + r₂ = -b/a

Product of Roots: r₁ × r₂ = c/a

Given one root, you can use these relationships to find the other root. The calculator uses these formulas to provide accurate results.

Worked Example

Let's solve the quadratic equation 2x² - 5x + 3 = 0 given that one root is 1.

Identify the coefficients: a = 2, b = -5, c = 3.
Use the sum of roots formula to find the other root:

1 + r₂ = -(-5)/2 = 5/2 = 2.5

r₂ = 2.5 - 1 = 1.5
Verify using the product of roots:

1 × 1.5 = 1.5

c/a = 3/2 = 1.5

The other root is 1.5.

Frequently Asked Questions

What is a quadratic equation?

A quadratic equation is a second-degree polynomial equation 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?

You can find the roots using the quadratic formula, factoring, or completing the square. This calculator uses the sum and product of roots formulas when one root is known.

What if the quadratic equation has complex roots?

If the discriminant (b² - 4ac) is negative, the roots will be complex numbers. This calculator can still find the roots, but they will be in the form of a + bi.

Can I use this calculator for higher-degree polynomials?

No, this calculator is specifically designed for quadratic equations. For higher-degree polynomials, you would need a different approach or calculator.