1. What is Quadratic Equation Factoring?

Factoring is the process of breaking down a quadratic equation into the product of two binomials. The general form is \( ax^2 + bx + c = a(x - r_1)(x - r_2) \), where \( r_1 \) and \( r_2 \) are the roots of the equation.

2. How Does the Calculator Work?

The calculator uses the quadratic formula to find roots:

Where:

• \( a \) — Coefficient of \( x^2 \)
• \( b \) — Coefficient of \( x \)
• \( c \) — Constant term

Explanation: The discriminant (\( b^2 - 4ac \)) determines the nature of the roots. If positive, two real roots; if zero, one real root; if negative, complex roots.

3. Importance of Factoring

Details: Factoring quadratic equations is fundamental in algebra, used for solving equations, graphing parabolas, and finding maximum/minimum values in real-world applications.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c of your quadratic equation. The calculator will provide the factored form and roots if they exist.

5. Frequently Asked Questions (FAQ)

Q1: What if the equation can't be factored?
A: The calculator will indicate if the equation has complex roots and cannot be factored with real coefficients.

Q2: What does a double root mean?
A: When the discriminant is zero, there's exactly one real root (a repeated root), and the parabola touches the x-axis at one point.

Q3: Can I factor equations with a=0?
A: No, this calculator is for quadratic equations (a≠0). For linear equations (a=0), use a different method.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places for clarity, but calculations use full precision.

Q5: What if I get complex roots?
A: Complex roots come in conjugate pairs and indicate the parabola doesn't intersect the x-axis.