Ruutvõrrandeid

Ruutvõrrandeid refers to quadratic equations in Estonian. A quadratic equation is a polynomial equation of the second degree. The general form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are coefficients and x is the unknown variable. The coefficient 'a' cannot be zero, otherwise, the equation would be linear.

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 Δ = b² - 4ac. If Δ > 0, there are two distinct real roots. If Δ = 0, there is exactly one real root (a repeated root). If Δ < 0, there are two complex conjugate roots.

The roots of a quadratic equation can be found using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a. This formula provides the values of x that satisfy the equation. Alternatively, quadratic equations can be solved by factoring, completing the square, or graphically by finding the x-intercepts of the corresponding parabola. Factoring is useful when the quadratic expression can be easily decomposed into two linear factors. Completing the square is a systematic method that can be used for any quadratic equation and is the basis for deriving the quadratic formula. Graphical solutions involve plotting the function y = ax² + bx + c and identifying where the graph intersects the x-axis.