Note that the quadratic formula actually has many real-world applications, such as calculating areas, projectile trajectories, and speed, among others. Alternative methods for solving quadratic equations do exist. Also shows the steps to solve and a graph below the solution. Solves an equation of the form ax2+bx+c0, a.k.a. This is demonstrated by the graph provided below. WolframAlpha Widgets: 'Quadratic Equation Solver' - Free Mathematics Widget. Furthermore, the quadratic formula also provides the axis of symmetry of the parabola.
The x values found through the quadratic formula are roots of the quadratic equation that represent the x values where any parabola crosses the x-axis.
Recall that the ± exists as a function of computing a square root, making both positive and negative roots solutions of the quadratic equation. Below is the quadratic formula, as well as its derivation.įrom this point, it is possible to complete the square using the relationship that:Ĭontinuing the derivation using this relationship: Only the use of the quadratic formula, as well as the basics of completing the square, will be discussed here (since the derivation of the formula involves completing the square). A quadratic equation can be solved in multiple ways, including factoring, using the quadratic formula, completing the square, or graphing. Hit the calculate button to get the roots. To solve an equation using the online calculator, simply enter the math problem in the text area provided. A quadratic is a second degree polynomial of the form: ax2 + bx + c 0 where a 0. For example, a cannot be 0, or the equation would be linear rather than quadratic. This quadratic equation root calculator lets you find the roots or zeroes of a quadratic equation.
The numerals a, b, and c are coefficients of the equation, and they represent known numbers. Where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. In algebra, a quadratic equation is any polynomial equation of the second degree with the following form: Solve any quadratic equation using the quadratic formula or the discriminant. The calculator on this page shows how the quadratic formula operates, but if you have access to a graphing calculator you should be able to solve quadratic equations, even ones with imaginary solutions. Fractional values such as 3/4 can be used.