Equations {quadratic equation} {second-degree equation} {quadric equation} can have one variable raised to second power. Quadratic equations have form a*x^2 + b*x + c = 0. Solution is x = (-b + (b^2 - 4*a*c)^0.5)/(2*a) and x = (-b - (b^2 - 4*a*c)^0.5)/(2*a). Quantity under square root is b^2 - 4*a*c {discriminant, quadratic equation}.
square
If quadratic equation has form a^2 * x^2 + b * x = c, add (b/(2*a))^2 to both equation sides {completing the square}. Factor left side: (a*x + b/(2*a))^2 = c. Take square root of both sides: a*x + b/(2*a) = c^0.5. Solve for x: x = (-b/(2*a) + c^0.5)/a.
factoring
If quadratic equation has form a*(x - r1)*(x - r2) = 0, then x = r1, x = r2, a = r1 + r2, and r1 * r2 = c/a.
graph
Quadratic-equation graph has U-shape.
Equations {cubic equation} can have variable raised to third power. General cubic equation has a solution.
Equations {quartic equation} can have variable raised to fourth power. General quartic equation has a solution.
General degree-higher-than-four equations {n-tic equation} do not have solutions.
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Date Modified: 2022.0225