neliöyhtälöinä

A "neliöyhtälö" is a mathematical equation of the second degree, meaning the highest power of the unknown variable is two. In its general form, it is written as ax² + bx + c = 0, where 'a', 'b', and 'c' are coefficients, and 'a' cannot be zero. The variable is typically represented by 'x'.

Solving a neliöyhtälö involves finding the values of 'x' that satisfy the equation. These values are called the roots or solutions of the equation. There can be zero, one, or two real roots, depending on the discriminant. The discriminant, denoted by Δ (delta), 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 no real roots, but there are two complex conjugate roots.

The roots of a neliöyhtälö can be found using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a. This formula directly applies the coefficients 'a', 'b', and 'c' to find the values of 'x'. Alternatively, neliöyhtälöt can sometimes be solved by factoring or by completing the square, especially when the coefficients are simple integers. Neliöyhtälöt have wide applications in various fields, including physics, engineering, and economics.