kvadratiivvõrrandi

A quadratic equation is a second-degree polynomial equation in a single variable. The general form of a quadratic equation is ax^2 + bx + c = 0, where x is the variable, and a, b, and c are coefficients. The coefficient 'a' cannot be zero, otherwise, the equation would be linear. The solutions to a quadratic equation are called roots.

There are several methods to solve quadratic equations. Factoring is one approach, where the quadratic expression is broken down into two linear factors. For example, if we have x^2 - 5x + 6 = 0, it can be factored into (x - 2)(x - 3) = 0, yielding roots x = 2 and x = 3. Completing the square is another method that transforms the equation into a perfect square trinomial, allowing for direct solution.

The most general method for solving quadratic equations is the quadratic formula. This formula provides the roots directly from the coefficients a, b, and c: x = [-b ± sqrt(b^2 - 4ac)] / 2a. The expression under the square root, b^2 - 4ac, is known as the discriminant. The value of the discriminant determines the nature of the roots. If the discriminant is positive, there are two distinct real roots. If it is zero, there is exactly one real root (a repeated root). If it is negative, there are two complex conjugate roots. Quadratic equations have wide applications in various fields, including physics, engineering, and economics, for modeling projectile motion, optimizing costs, and analyzing growth patterns.