Quadratic Roots Calculator Ti 30xs

How to Use This Calculator

To use the quadratic roots calculator for the TI-30XS, follow these simple steps:

1. Enter the coefficients of your quadratic equation in the form ax² + bx + c = 0.
2. Click the "Calculate" button to find the roots.
3. Review the results and the step-by-step solution.
4. Use the chart to visualize the quadratic function.

The calculator will display both roots (real or complex) and show how to solve the equation using the quadratic formula.

Quadratic Formula

The quadratic formula is used to find the roots of any quadratic equation in the form ax² + bx + c = 0:

Where:

• a, b, and c are the coefficients of the quadratic equation
• √(b² - 4ac) is the discriminant
• The ± symbol indicates there are two roots

The discriminant determines the nature of the roots:

• If b² - 4ac > 0: Two distinct real roots
• If b² - 4ac = 0: One real root (repeated)
• If b² - 4ac < 0: Two complex conjugate roots

Worked Examples

Example 1: Simple Quadratic Equation

Solve x² - 5x + 6 = 0

1. Identify coefficients: a=1, b=-5, c=6
2. Calculate discriminant: (-5)² - 4(1)(6) = 25 - 24 = 1
3. Apply quadratic formula: x = [5 ± √1]/2
4. Find roots: x = (5+1)/2 = 3 and x = (5-1)/2 = 2

Example 2: Complex Roots

Solve x² + 2x + 5 = 0

1. Identify coefficients: a=1, b=2, c=5
2. Calculate discriminant: (2)² - 4(1)(5) = 4 - 20 = -16
3. Apply quadratic formula: x = [-2 ± √(-16)]/2
4. Find roots: x = -1 ± 2i (complex roots)