Whakaoti i te 0=b^2-4ac

$$0 = b ^ { 2 } - 4 a c$$

Whakaoti mō a (complex solution)

$$\left\{\begin{matrix}a=\frac{b^{2}}{4c}\text{, }&c\neq 0\\a\in \mathrm{C}\text{, }&b=0\text{ and }c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$b^{2}-4ac=0$$

Tangohia te b^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-4ac=-b^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-4c\right)a=-b^{2}$$

Whakawehea ngā taha e rua ki te -4c.

$$\frac{\left(-4c\right)a}{-4c}=-\frac{b^{2}}{-4c}$$

Mā te whakawehe ki te -4c ka wetekia te whakareanga ki te -4c.

$$a=-\frac{b^{2}}{-4c}$$

Whakawehe -b^{2} ki te -4c.

$$a=\frac{b^{2}}{4c}$$

Whakaoti mō a

$$\left\{\begin{matrix}a=\frac{b^{2}}{4c}\text{, }&c\neq 0\\a\in \mathrm{R}\text{, }&b=0\text{ and }c=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$b^{2}-4ac=0$$

Tangohia te b^{2} mai i ngā taha e rua. Ko te tau i tango i te kore ka hua ko tōna korenga.

$$-4ac=-b^{2}$$

He hanga arowhānui tō te whārite.

$$\left(-4c\right)a=-b^{2}$$

Whakawehea ngā taha e rua ki te -4c.

$$\frac{\left(-4c\right)a}{-4c}=-\frac{b^{2}}{-4c}$$

Mā te whakawehe ki te -4c ka wetekia te whakareanga ki te -4c.

$$a=-\frac{b^{2}}{-4c}$$

Whakawehe -b^{2} ki te -4c.

$$a=\frac{b^{2}}{4c}$$

Whakaoti mō b (complex solution)

$$b=-2\sqrt{a}\sqrt{c}$$

$$b=2\sqrt{a}\sqrt{c}$$

Whakaoti mō b

$$b=2\sqrt{ac}$$

$$b=-2\sqrt{ac}\text{, }\left(c\geq 0\text{ and }a\geq 0\right)\text{ or }\left(a\leq 0\text{ and }c\leq 0\right)$$