Factor Trinomial Calculator

How to Use the Factor Trinomial Calculator

This guide will walk you through the steps to effectively use the Factor Trinomial Calculator to find the roots and factors of a quadratic trinomial in the form ax² + bx + c.

Step 1: Input Coefficients

• Coefficient a: Locate the input field labeled “Coefficient a (ax²)”. Enter the coefficient of the x² term in your trinomial. This value is required and must be between -999999 and 999999. You should enter an integer as the step is 1.
• Coefficient b: Find the “Coefficient b (bx)” field. Here, input the coefficient of the x term from your trinomial. Like coefficient a, this entry is mandatory and should also be an integer ranging from -999999 to 999999.
• Constant c: Identify the “Constant c” field. Enter the constant term of your trinomial equation. Again, this value is necessary and must adhere to the same range and integer value restrictions as the other coefficients.

Step 2: Calculate

Once all input fields are filled correctly, the calculator processes these values to deliver the necessary results. There is no separate button press or action needed; results appear automatically.

Step 3: Interpret the Results

• Discriminant: The discriminant of the trinomial is calculated using the formula b² – 4ac. The result will be displayed with two decimal places. This value determines the nature of the roots. A positive discriminant indicates two distinct roots, zero indicates one real root, and a negative discriminant implies complex roots.
• Roots: The calculator computes the roots of the trinomial using the quadratic formula. You will see:
  • First Root: Calculated as ((-b + sqrt{b² – 4ac}) / (2a)) and displayed to four decimal places.
  • Second Root: Calculated as ((-b – sqrt{b² – 4ac}) / (2a)) and also presented with four decimal places.
• Factors: The trinomial’s expression in factored form is shown:
  • First Factor: If (a = 1), the factor is expressed as (x + root1). Otherwise, it is expressed as (ax + -root1 * a).
  • Second Factor: Similarly, if (a = 1), the factor is (x + root2). Otherwise, it becomes (ax + -root2 * a).

Ensure you interpret the results according to your specific equation, and use this information for further analysis or problem-solving tasks.