Máy Giải Phương Trình

Q: What is the discriminant?

The discriminant (b² - 4ac) determines the nature of quadratic equation solutions. Positive means two real solutions, zero means one repeated solution, and negative means no real solutions (complex numbers).

Q: Can this solver handle equations with no solution?

Yes. For equations like 0x = 5 (no solution) or 0x = 0 (infinite solutions), the solver will indicate the appropriate result.

Stuck on algebra homework? Enter any linear or quadratic equation and get the answer plus a full step-by-step breakdown — not just the result, but exactly how you get there.

Máy Giải Phương Trình là gì?

An equation solver finds the values of variables that satisfy mathematical equations. From simple linear equations to complex quadratic and polynomial equations, this tool helps you solve algebraic problems quickly and accurately. Whether you're a student checking homework, a teacher preparing lessons, or a professional solving real-world problems, an equation solver is an indispensable resource.

Linear equations (ax + b = 0) have one solution, quadratic equations (ax² + bx + c = 0) can have up to two solutions, and higher-degree polynomials can have multiple solutions. The equation solver uses proven mathematical methods like the quadratic formula, factoring, and numerical approximation to find exact or approximate solutions.

Công Thức

Linear: ax + b = 0 → x = -b/a

Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a

Discriminant: Δ = b² - 4ac

Δ > 0: Two real solutions

Δ = 0: One real solution

Δ < 0: No real solutions (complex)

Cách Tính

Select the type of equation (linear, quadratic, etc.).
Enter the coefficients (a, b, c, etc.).
Click solve to find the solution(s).
View the step-by-step solution process.
Verify the solution by substituting back into the equation.

Ví Dụ

Solving 2x² - 5x + 2 = 0: a=2, b=-5, c=2. Discriminant: (-5)² - 4(2)(2) = 25 - 16 = 9. x = [5 ± √9] / 4 = [5 ± 3] / 4. Solutions: x = 2 or x = 0.5. Checking: 2(2)² - 5(2) + 2 = 8 - 10 + 2 = 0 ✓

Lợi Ích Chính

Solve linear quadratic polynomial step by step
Handle multi-variable equation systems
Verify solutions catch errors
Visualize variable relationships

Những Lỗi Thường Gặp Cần Tránh

Not same operation on both sides
Losing solutions dividing by zero variable
Wrong quadratic formula coefficient signs

Mẹo Chuyên Nghiệp

Check by substituting back
Try factoring quadratics first
Verify all equations not just one

Các Thuật Ngữ Chính Được Giải Thích

Biến: Symbol for unknown value
Công thức bậc hai: x equals negative b plus minus root
Đẳng thức: Determines solution count
Hệ phương trình: Multiple solved together

Trường Hợp Sử Dụng Phổ Biến

Solving algebra homework and practice problems
Finding break-even points in business calculations
Determining roots of polynomial functions in engineering
Checking manual calculations for accuracy

Câu Hỏi Thường Gặp

What is the discriminant?

The discriminant (b² - 4ac) determines the nature of quadratic equation solutions. Positive means two real solutions, zero means one repeated solution, and negative means no real solutions (complex numbers).

Can this solver handle equations with no solution?

Yes. For equations like 0x = 5 (no solution) or 0x = 0 (infinite solutions), the solver will indicate the appropriate result.