Factoring a Quadratic Calculator

Quadratic Equation:

\[ ax^2 + bx + c = 0 \]

Factored Form:

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1. What is Factoring a Quadratic?

Factoring a quadratic equation means expressing it as a product of two binomials. For a quadratic equation in the form \( ax^2 + bx + c = 0 \), factoring helps find its roots and understand its behavior.

2. How Does the Calculator Work?

The calculator uses the quadratic formula to find roots:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Where:

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

Explanation: The calculator finds the roots r and s, then expresses the quadratic in factored form as \( (x - r)(x - s) \).

3. Importance of Factoring Quadratics

Details: Factoring is essential for solving quadratic equations, analyzing parabolic graphs, and understanding the behavior of quadratic functions in mathematics and physics applications.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will provide the factored form. Note: a cannot be zero for a quadratic equation.

5. Frequently Asked Questions (FAQ)

Q1: What if the quadratic has complex roots?
A: The calculator will indicate that the equation has complex roots and cannot be factored over real numbers.

Q2: Can I factor quadratics with decimal coefficients?
A: Yes, the calculator handles decimal coefficients and provides results with appropriate precision.

Q3: What about perfect square trinomials?
A: The calculator correctly identifies and factors perfect square trinomials as \( (x - r)^2 \).

Q4: How are negative roots handled in the factored form?
A: Negative roots are displayed with plus signs (e.g., (x + 3) for root -3).

Q5: Can this calculator handle quadratic equations with a=1?
A: Yes, the calculator works for all quadratic equations regardless of the value of a (as long as a ≠ 0).