Solve f(x)leq0=ax^2+bx+c

$$f ( x ) \leq 0 = a x ^ { 2 } + b x + c$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{bx+c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx+c=0$$

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}+c=-bx$$

Subtract c from both sides.

$$ax^{2}=-bx-c$$

The equation is in standard form.

$$x^{2}a=-bx-c$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{-bx-c}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{-bx-c}{x^{2}}$$

Divide -bx-c by x^{2}.

$$a=-\frac{bx+c}{x^{2}}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=-ax-\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx+c=0$$

Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.

$$bx+c=-ax^{2}$$

Subtract c from both sides.

$$bx=-ax^{2}-c$$

The equation is in standard form.

$$xb=-ax^{2}-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-ax^{2}-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-ax^{2}-c}{x}$$

Divide -ax^{2}-c by x.

$$b=-ax-\frac{c}{x}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{bx+c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx+c=0$$

Subtract bx from both sides. Anything subtracted from zero gives its negation.

$$ax^{2}+c=-bx$$

Subtract c from both sides.

$$ax^{2}=-bx-c$$

The equation is in standard form.

$$x^{2}a=-bx-c$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{-bx-c}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{-bx-c}{x^{2}}$$

Divide -bx-c by x^{2}.

$$a=-\frac{bx+c}{x^{2}}$$

Solve for b

$$\left\{\begin{matrix}b=-ax-\frac{c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&c=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx+c=0$$

Subtract ax^{2} from both sides. Anything subtracted from zero gives its negation.

$$bx+c=-ax^{2}$$

Subtract c from both sides.

$$bx=-ax^{2}-c$$

The equation is in standard form.

$$xb=-ax^{2}-c$$

Divide both sides by x.

$$\frac{xb}{x}=\frac{-ax^{2}-c}{x}$$

Dividing by x undoes the multiplication by x.

$$b=\frac{-ax^{2}-c}{x}$$

Divide -ax^{2}-c by x.

$$b=-ax-\frac{c}{x}$$