Overview
This lecture explains how to write and structure a program to solve quadratic equations, focusing on variable setup, discriminant calculation, solution logic, and user input/output.
Variable Declaration and Initialization
- Coefficients a, b, and c represent the quadratic equation terms and are provided by the user.
- Variables delta (discriminant), x1, and x2 are declared for solution calculations.
- All variables are initialized with "neutral" or placeholder values at program start.
- Data types for variables are chosen to match their expected values (typically integers).
Discriminant Calculation
- The discriminant (delta) is calculated with the formula: delta = b² - 4ac.
- This calculation uses the values entered by the user for a, b, and c.
Conditional Logic for Solutions
- A conditional (if-else) statement checks the value of delta to determine the number of solutions:
- If delta is negative, display "This equation has no solution."
- If delta is zero, compute x1 = -b / (2a) and display "The equation has only one solution: x1."
- Otherwise (delta positive), compute:
- x1 = (-b - sqrt(delta)) / (2a)
- x2 = (-b + sqrt(delta)) / (2a)
- Display "The equation has two solutions: x1 and x2."
User Interaction and Output
- The user is prompted to enter values for a, b, and c via the keyboard.
- The program displays the result message and value(s) according to discriminant outcome.
Testing and Validation
- The program should be tested with known input values to verify calculations are correct.
Key Terms & Definitions
- Quadratic Equation — An equation in the form ax² + bx + c = 0.
- Coefficient — A numerical factor (a, b, or c) in the equation.
- Discriminant (delta) — The value b² - 4ac, determining the number and type of solutions.
- Solution (x1, x2) — The values of x that satisfy the equation.
Action Items / Next Steps
- Complete and compile the program as described.
- Test the program with various known cases to validate correctness.