Quadratic Equations Solver
Understanding Quadratic Equations
A quadratic equation is a second-degree polynomial equation of the form $ax^2 + bx + c = 0$, where $a, b, c$ are coefficients and $a \neq 0$. The solutions to this equation are called roots.
This explorer provides various methods to solve quadratic equations:
- Quadratic Formula: A direct formula to find the roots.
- Completing the Square: A method to transform the equation into a perfect square trinomial.
- Factorization: Expressing the quadratic as a product of two linear factors (if possible with simple roots).
- Graphical Method: Finding roots by identifying the x-intercepts of the parabola $y = ax^2 + bx + c$.
Solving by Quadratic Formula
The quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ finds the roots of $ax^2 + bx + c = 0$.
Solving by Completing the Square
This method involves transforming $ax^2 + bx + c = 0$ into the form $(x+p)^2 = q$.
Solving by Factorization
Factor the quadratic $ax^2 + bx + c$ into two linear factors. This method is most straightforward for equations with integer or simple rational roots.
Solving by Graphical Method
The real roots of $ax^2 + bx + c = 0$ are the x-intercepts of the parabola $y = ax^2 + bx + c$.