Solve Quadratic Equation by Using The Square Root Property Calculator

Introduction

Quadratic equations are equations of the form \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants. The square root property is a specific method used to solve quadratic equations that can be rewritten in the form \(x^2 = a\).

This property states that if \(x^2 = a\), then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\). This means that the solutions to the equation are the positive and negative square roots of \(a\).

How to Use the Calculator

Using the calculator is simple:

1. Enter the value of \(a\) in the input field.
2. Click the "Calculate" button.
3. The calculator will display the solutions \(x = \sqrt{a}\) and \(x = -\sqrt{a}\).

The calculator also provides a visual representation of the solutions using Chart.js.

The Square Root Property Formula

This formula is derived from the definition of square roots. The square root of a number \(a\) is a number \(x\) such that \(x^2 = a\). Since squaring both the positive and negative roots of \(a\) yields \(a\), both solutions are valid.

Worked Examples

Example 1

Solve \(x^2 = 16\).

Using the square root property:

\(x = \sqrt{16}\) or \(x = -\sqrt{16}\)

\(x = 4\) or \(x = -4\)

The solutions are \(x = 4\) and \(x = -4\).

Example 2

Solve \(x^2 = 9\).

Using the square root property:

\(x = \sqrt{9}\) or \(x = -\sqrt{9}\)

\(x = 3\) or \(x = -3\)

The solutions are \(x = 3\) and \(x = -3\).