Whakaoti i te eta=ax^2+bx+c

$$\eta = a x ^ { 2 } + b x + c$$

Whakaoti mō a (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ax^{2}+bx+c=\eta$$

Tangohia te bx mai i ngā taha e rua.

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

Tangohia te c mai i ngā taha e rua.

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

He hanga arowhānui tō te whārite.

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

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

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

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

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

Whakaoti mō b (complex solution)

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ax^{2}+bx+c=\eta$$

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

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

Tangohia te c mai i ngā taha e rua.

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

Whakaraupapatia anō ngā kīanga tau.

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

He hanga arowhānui tō te whārite.

$$xb=-ax^{2}+\eta -c$$

Whakawehea ngā taha e rua ki te x.

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

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

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

Whakaoti mō a

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ax^{2}+bx+c=\eta$$

Tangohia te bx mai i ngā taha e rua.

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

Tangohia te c mai i ngā taha e rua.

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

He hanga arowhānui tō te whārite.

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

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

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

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

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

Whakaoti mō b

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$ax^{2}+bx+c=\eta$$

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

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

Tangohia te c mai i ngā taha e rua.

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

Whakaraupapatia anō ngā kīanga tau.

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

He hanga arowhānui tō te whārite.

$$xb=-ax^{2}+\eta -c$$

Whakawehea ngā taha e rua ki te x.

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

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

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