Algebra Calculator
Solve quadratic equations, linear equations, systems, and more
Algebra Calculations
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Solve ax² + bx + c = 0
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About Algebra Calculations
Quadratic Equations
- • Discriminant `>` 0: Two distinct real roots
- • Discriminant = 0: One real root (repeated)
- • Discriminant `<` 0: Two complex roots
- • Vertex: Minimum or maximum point of the parabola
Linear Equations
- • Slope: Rate of change (rise over run)
- • Y-Intercept: Point where line crosses y-axis
- • X-Intercept: Point where line crosses x-axis
Systems of Equations
- • Unique Solution: Lines intersect at one point
- • Infinite Solutions: Lines are identical
- • No Solution: Lines are parallel
Frequently Asked Questions
How do you solve a quadratic equation?▾
Use the quadratic formula x = (−b ± √(b² − 4ac)) / 2a for ax² + bx + c = 0. You can also factor, complete the square, or graph the equation to find the roots.
What is the discriminant?▾
The discriminant is b² − 4ac in a quadratic equation. If positive, the equation has two real roots; if zero, one real root; if negative, two complex roots.
How do you solve a system of linear equations?▾
Common methods are substitution (solve one equation for a variable and substitute into the other), elimination (add or subtract equations), and matrix methods like Cramer's rule.
What does it mean to factor an expression?▾
Factoring rewrites an expression as a product of simpler terms. For example, x² − 4 factors into (x − 2)(x + 2). Factoring makes it easier to find roots and simplify expressions.