Quadratic Formula Calculator

How to Use the Quadratic Formula Calculator

The Quadratic Formula Calculator is a helpful tool that assists you in solving quadratic equations of the form ax² + bx + c = 0. Follow the step-by-step guide below to effectively utilize the calculator and find the roots of your quadratic equations.

Step 1: Enter the Coefficients

• Coefficient a: Locate the input field labeled “Coefficient a.” Enter the value of the coefficient a, ensuring it is not zero (as a should be non-zero in a quadratic equation). The field allows numbers ranging from -1,000,000 to 1,000,000.
• Coefficient b: Locate the input field labeled “Coefficient b.” Enter the value of coefficient b within the specified range of -1,000,000 to 1,000,000.
• Coefficient c: Locate the input field labeled “Coefficient c.” Enter the value of coefficient c also within the specified range of -1,000,000 to 1,000,000.

Step 2: Understanding the Results

Once you’ve entered the coefficients, the calculator will automatically compute and display the results based on the quadratic formula. The results include:

• Discriminant: The discriminant is calculated using the formula b² – 4ac. It helps determine the nature of the roots and is displayed with up to four decimal places.
• First Root (x₁): This is calculated as (−b + √(b² – 4ac))/(2a) and is presented with up to four decimal places.
• Second Root (x₂): Calculated using the formula (−b – √(b² – 4ac))/(2a), this result is also shown to four decimal places.
• Type of Roots: Based on the value of the discriminant, this field indicates whether the quadratic equation has “Two Real Roots,” “One Real Root (Double Root),” or “Two Complex Roots.”

Step 3: Interpreting the Results

Use the results provided by the calculator to understand the solution to your quadratic equation:

• If the discriminant is greater than zero, the equation has two distinct real roots.
• If the discriminant equals zero, the equation has a double root, meaning both roots are real and equal.
• If the discriminant is less than zero, the equation has two complex roots.

By following these steps, you can easily find the solutions to any quadratic equation using the Quadratic Formula Calculator. Whether you are a student, educator, or professional, this calculator serves as a reliable tool for solving quadratic equations efficiently.