static float A; static float B; static float C; static float delta; static float x1, x2, x3; static float x2_real, x3_real, x2_virtual, x3_virtual; static float deltaQuadratic; /// <summary> /// 盛金公式求解一元三次方程 /// </summary> /// <param name="a">三次系数</param> /// <param name="b">二次系数</param> /// <param name="c">一次系数</param> /// <param name="d">常系数</param> /// <param name="r1">结果1 为null则没有实根</param> /// <param name="r2">结果2</param> /// <param name="r3">结果3</param> private static void solveEquations(float a, float b, float c, float d, out float r1, out float r2, out float r3) { r1 = 0; r2 = 0; r3 = 0; A = b * b - 3 * a * c; B = b * c - 9 * a * d; C = c * c - 3 * b * d; delta = B * B - 4 * A * C; if (d == 0) { x3 = 0; solveQuadraticEquation(a, b, c, d); } else if (A == 0 && B == 0) { x1 = -b / (3 * a); x2 = -c / b; x3 = -3 * d / c; } else if (delta > 0) { float Y1 = float.Parse((A * b + 3 * a * (-B + Math.Sqrt(delta)) / 2).ToString()); float Y2 = float.Parse((A * b + 3 * a * (-B - Math.Sqrt(delta)) / 2).ToString()); x1 = (-b - (getCubeRoot(Y1) + getCubeRoot(Y2))) / (3 * a); x3_real = x2_real = (-b + getCubeRoot(Y1)) / (3 * a); x2_virtual = float.Parse((((Math.Sqrt(3) / 2) * (getCubeRoot(Y1) - getCubeRoot(Y2))) / (3 * a)).ToString()); x3_virtual = -x2_virtual; } else if (delta == 0) { var K = B / A; //A != 0 x1 = -b / a + K; x2 = x3 = -K / 2; } else { //delta < 0 var T = (2 * A * b - 3 * a * B) / (2 * Math.Sqrt(A * A * A)); // A > 0, -1 < T < 1 var angle = Math.Acos(T) / 3; x1 = float.Parse(((-b - 2 * Math.Sqrt(A) * Math.Cos(angle)) / (3 * a)).ToString()); x2 = float.Parse(((-b + Math.Sqrt(A) * (Math.Cos(angle) + Math.Sqrt(3) * Math.Sin(angle))) / (3 * a)).ToString()); x3 = float.Parse(((-b + Math.Sqrt(A) * (Math.Cos(angle) - Math.Sqrt(3) * Math.Sin(angle))) / (3 * a)).ToString()); } if (A == 0 && B == 0) { //方程有一个三重实根 r1 = x1; r2 = x1; r3 = x1; return; } else if (delta > 0) { //方程有一个实根和一对共轭虚根 r1 = x1; r2 = x2_real + x2_virtual; r3 = x2_real + x2_virtual; } else if (delta == 0) { //方程有一个实根，其中有一个两重根 r1 = x1; r2 = x2; r3 = x2; } else { //方程有三个不相等的实根 r1 = x1; r2 = x2; r3 = x3; } } private static void solveQuadraticEquation(float a, float b, float c, float d) { deltaQuadratic = b * b - 4 * a * c; if (deltaQuadratic == 0) { x1 = x2 = -b / (2 * a); } else if (deltaQuadratic > 0) { x1 = -b + float.Parse((Math.Sqrt(deltaQuadratic) / (2 * a)).ToString()); x2 = -b - float.Parse((Math.Sqrt(deltaQuadratic) / (2 * a)).ToString()); } else { x2_real = -b / (2 * a); x2_virtual = float.Parse((Math.Sqrt(-deltaQuadratic) / (2 * a)).ToString()); } } private static float getCubeRoot(float value) { if (value < 0) { return float.Parse((-Math.Pow(-value, 1f / 3)).ToString()); } else if (value == 0) { return 0; } else { return float.Parse(Math.Pow(value, 1f / 3).ToString()); } }
调用solveEquations方法即可。