Solve f(x)=x^3+kappax+lambda,kappa,lambdainR

$$f ( x ) = x ^ { 3 } + \kappa x + \lambda , \kappa , \lambda \in R$$

Solve for f

$$\left\{\begin{matrix}f=x^{2}+\kappa +\frac{\lambda }{x}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&x=0\text{ and }\lambda =0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$xf=x^{3}+x\kappa +\lambda$$

Divide both sides by x.

$$\frac{xf}{x}=\frac{x^{3}+x\kappa +\lambda }{x}$$

Dividing by x undoes the multiplication by x.

$$f=\frac{x^{3}+x\kappa +\lambda }{x}$$

Divide \lambda +x^{3}+x\kappa by x.

$$f=x^{2}+\kappa +\frac{\lambda }{x}$$