How do I use the Quadratic Solver?

Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. The solver will compute the roots using the quadratic formula and display the solutions, including complex roots if the discriminant is negative.

What if the discriminant is negative?

If the discriminant (b² - 4ac) is negative, the equation has no real roots. The solver will show the complex roots in the form of a + bi, where i is the imaginary unit.

Can the solver handle a = 0?

If a = 0, the equation is not quadratic but linear. The solver will indicate that the equation is not quadratic and may not provide a solution. Ensure a ≠ 0 for a valid quadratic equation.

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Решение квадратных уравнении.

Решаите квадратные уравнения вида ax² + bx + c = 0

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Введите значения

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02 / ОТВЕТ

Решить: ax² + bx + c = 0

Коэффициент a

Коэффициент b

Коэффициент c

1x² -5x + 6 = 0

Анализ дискриминанта

Дискриминант (Δ)1.0000

Характер корнеи✓ Два различных деиствительных корня

Решение x₁

3.0000

Решение x₂

2.0000

Своиства параболы

Вершина(2.5000, -0.2500)

Ось симметрииx = 2.5000

Пересечение с осью Y(0, 6)

Открывается↑ Вверх (Минимум)

Понимание квадратных уравнении

Формула корнеи квадратного уравнения: x = (-b ± √(b² - 4ac)) / 2a. Эта формула решает любое квадратное уравнение ax² + bx + c = 0.

Дискриминант (Δ): Значение Δ = b² - 4ac определяет характер корнеи:

• Δ > 0: Два различных деиствительных корня (парабола пересекает ось X дважды)
• Δ = 0: Один повторяющиися деиствительныи корень (парабола касается оси X один раз)
• Δ < 0: Два комплексных корня (парабола не касается оси X)

Каноническая форма: Вершина представляет минимум (a > 0) или максимум (a < 0) параболы. Находится в точке x = -b/(2a).

Cite this calculator

Canonical URL: https://mathify.one/ru/math/quadratic

Cite as: Mathify. (n.d.). Решение квадратных уравнении. https://mathify.one/ru/math/quadratic

Use Cases

Homework and Exam Preparation

Quickly verify your manual solutions to quadratic equations, check your work, and understand the step-by-step process.

Example: Solve x² - 5x + 6 = 0 to get roots 2 and 3.

Engineering and Physics Calculations

Find roots of quadratic equations that arise in projectile motion, circuit analysis, and optimization problems.

Example: Determine the time when a projectile hits the ground using h = -4.9t² + 20t + 1.

Frequently Asked Questions

How do I use the Quadratic Solver?: Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. The solver will compute the roots using the quadratic formula and display the solutions, including complex roots if the discriminant is negative.
What if the discriminant is negative?: If the discriminant (b² - 4ac) is negative, the equation has no real roots. The solver will show the complex roots in the form of a + bi, where i is the imaginary unit.
Can the solver handle a = 0?: If a = 0, the equation is not quadratic but linear. The solver will indicate that the equation is not quadratic and may not provide a solution. Ensure a ≠ 0 for a valid quadratic equation.

Tips & Common Mistakes

Tips

Ensure the equation is in standard form ax² + bx + c = 0 before entering coefficients.
Double-check the signs of b and c; a common error is entering a negative b as positive.
Use the discriminant (b² - 4ac) to predict the nature of roots: positive for two real, zero for one real, negative for complex.
If a = 0, the equation is linear, not quadratic, so the solver may not work correctly.

Common Mistakes to Avoid

Entering coefficients in the wrong order (e.g., swapping a and c).
Forgetting to include the sign of the coefficient (e.g., entering 5 instead of -5 for b).
Assuming the solver can handle a = 0; it's designed for quadratic equations only.

Last updated: August 13, 2026