Raiz maior ax²+bx+c=0
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Quadratic Polynomial Largest Root Calculator is an online tool that allows you to find the largest root of a quadratic equation of the form ax² + bx + c = 0. The formula used is x₁ = (−b+√Δ)/(2a), where Δ is the discriminant, calculated as b² - 4ac. This calculator is useful for solving problems involving quadratic equations in various fields such as physics, engineering, and economics.
The formula x₁ = (−b+√Δ)/(2a) works as follows: first, the discriminant Δ is calculated, which determines the nature of the roots. If Δ is positive, there are two distinct real roots; if it is zero, there is one real root; and if it is negative, there are two complex conjugate roots. The calculator then uses the value of Δ to calculate the largest root of the equation.
It is essential to use this calculator in cases where the quadratic equation has a real solution and you need to find the largest root. For example, in physics problems involving uniformly varied motion, the roots of the quadratic equation can represent the moments when an object passes through a certain position. Another case is in engineering, where the roots can represent natural frequencies of a system.
When using the calculator, it is crucial to be careful with the input values of a, b, and c, ensuring they are real numbers and that a is not zero, as the equation loses its quadratic character if a is zero. Additionally, it is always a good idea to check if the obtained values make sense in the context of the problem being solved.
Frequently asked questions
What is the discriminant Δ and how does it affect the roots of the equation?
The discriminant Δ is calculated as b² - 4ac and determines the nature of the roots of the quadratic equation. If Δ is positive, there are two distinct real roots; if it is zero, there is one real root; and if it is negative, there are two complex conjugate roots.
Can I use this calculator for equations that do not have real solutions?
Yes, the calculator can handle equations that have complex roots. In this case, the result will be a pair of complex conjugate roots.
How can I know if the found root is the largest?
The calculator explicitly states the largest root of the equation. If you want to check, you can compare it with the other root, which can be found with the formula x₂ = (−b-√Δ)/(2a).
Is the calculator suitable for linear equations?
No, this calculator is specifically designed for quadratic equations (of second degree). Linear equations (of first degree) have a different form and are solved in a different way.