Whakaoti i te x^3+ax^2+bx+c=0

$$x ^ { 3 } + a x ^ { 2 } + b x + c = 0$$

Whakaoti mō a

$$\left\{\begin{matrix}a=-\frac{x^{3}+bx+c}{x^{2}}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x^{3} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$ax^{2}+bx+c=-x^{3}$$

Tangohia te bx mai i ngā taha e rua.

$$ax^{2}+c=-x^{3}-bx$$

Tangohia te c mai i ngā taha e rua.

$$ax^{2}=-x^{3}-bx-c$$

He hanga arowhānui tō te whārite.

$$x^{2}a=-x^{3}-bx-c$$

Whakawehea ngā taha e rua ki te x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{-x^{3}-bx-c}{x^{2}}$$

Mā te whakawehe ki te x^{2} ka wetekia te whakareanga ki te x^{2}.

$$a=\frac{-x^{3}-bx-c}{x^{2}}$$

Whakawehe -x^{3}-bx-c ki te x^{2}.

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

Whakaoti mō b

$$\left\{\begin{matrix}b=-\frac{x^{3}+ax^{2}+c}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tangohia te x^{3} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$ax^{2}+bx+c=-x^{3}$$

Tangohia te ax^{2} mai i ngā taha e rua.

$$bx+c=-x^{3}-ax^{2}$$

Tangohia te c mai i ngā taha e rua.

$$bx=-x^{3}-ax^{2}-c$$

He hanga arowhānui tō te whārite.

$$xb=-x^{3}-ax^{2}-c$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xb}{x}=\frac{-x^{3}-ax^{2}-c}{x}$$

Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.

$$b=\frac{-x^{3}-ax^{2}-c}{x}$$

Whakawehe -x^{3}-ax^{2}-c ki te x.

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