Kvadratiivvõrrandid

Kvadratiivvõrrandid are algebraic equations of the second degree. The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are coefficients, and 'a' cannot be zero. The variable 'x' is the unknown we aim to solve for.

The solutions to a quadratic equation are called roots. There can be zero, one, or two distinct real roots, or two complex conjugate roots. The nature and number of roots are determined by the discriminant, which is calculated as delta = b^2 - 4ac. If delta > 0, there are two distinct real roots. If delta = 0, there is exactly one real root (a repeated root). If delta < 0, there are two complex conjugate roots.

The most common method for solving quadratic equations is the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a. This formula directly provides the values of x that satisfy the equation. Another method is completing the square, which involves manipulating the equation to form a perfect square trinomial. Factoring is also applicable when the quadratic expression can be easily factored into two linear expressions.

Quadratic equations appear in various mathematical and scientific contexts, including physics (e.g., projectile motion), engineering, and economics, due to their ability to model parabolic relationships and optimize functions.