Algebra Calculator
Solve linear and quadratic equations
Table of Contents
How to Use
- Select the equation type (linear or quadratic)
- Enter the coefficient values (a, b, and c for quadratic)
- Click 'Calculate' to see the solution
- Review the step-by-step explanation
Frequently Asked Questions
- What's the difference between linear and quadratic equations?
- Linear equations have variables raised to the first power (x) and produce a straight line when graphed. They have exactly one solution. Quadratic equations have variables raised to the second power (x²) and produce a parabola when graphed. They can have zero, one, or two real solutions depending on the discriminant.
- What is the discriminant in quadratic equations?
- The discriminant is the expression b² - 4ac found under the square root in the quadratic formula. It determines how many and what type of solutions the equation has. A positive discriminant means two real solutions, zero means one solution, and negative means no real solutions (but two complex solutions).
- What does it mean when the discriminant is negative?
- When the discriminant is negative, the quadratic equation has no real number solutions. Instead, it has two complex (imaginary) solutions. Graphically, this means the parabola does not cross the x-axis. In real-world problems, this often indicates that the problem has no physical solution under the given constraints.
- How do I know which equation type to use?
- Use a linear equation when your problem involves a constant rate of change or direct proportionality. Use a quadratic equation when your problem involves acceleration, area calculations, projectile motion, or any situation where the relationship involves squaring a variable. Look for keywords like 'area,' 'squared,' 'parabola,' or situations involving gravity or acceleration.