Whakaoti i te (x+1)(x-3)=x^2+mx+n

$$( x + 1 ) ( x - 3 ) = x ^ { 2 } + m x + n$$

Whakaoti mō m (complex solution)

$$\left\{\begin{matrix}m=-\frac{2x+n+3}{x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&x=0\text{ and }n=-3\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te x-3 ka whakakotahi i ngā kupu rite.

$$x^{2}-2x-3=x^{2}+mx+n$$

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

$$x^{2}+mx+n=x^{2}-2x-3$$

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

$$mx+n=x^{2}-2x-3-x^{2}$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$mx+n=-2x-3$$

Tangohia te n mai i ngā taha e rua.

$$mx=-2x-3-n$$

He hanga arowhānui tō te whārite.

$$xm=-2x-n-3$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xm}{x}=\frac{-2x-n-3}{x}$$

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

$$m=\frac{-2x-n-3}{x}$$

Whakawehe -2x-3-n ki te x.

$$m=-\frac{2x+n+3}{x}$$

Whakaoti mō m

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

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te x-3 ka whakakotahi i ngā kupu rite.

$$x^{2}-2x-3=x^{2}+mx+n$$

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

$$x^{2}+mx+n=x^{2}-2x-3$$

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

$$mx+n=x^{2}-2x-3-x^{2}$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$mx+n=-2x-3$$

Tangohia te n mai i ngā taha e rua.

$$mx=-2x-3-n$$

He hanga arowhānui tō te whārite.

$$xm=-2x-n-3$$

Whakawehea ngā taha e rua ki te x.

$$\frac{xm}{x}=\frac{-2x-n-3}{x}$$

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

$$m=\frac{-2x-n-3}{x}$$

Whakawehe -2x-3-n ki te x.

$$m=-\frac{2x+n+3}{x}$$

Whakaoti mō n

$$n=-\left(mx+2x+3\right)$$

Ngā Upane Otinga

Whakamahia te āhuatanga tuaritanga hei whakarea te x+1 ki te x-3 ka whakakotahi i ngā kupu rite.

$$x^{2}-2x-3=x^{2}+mx+n$$

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

$$x^{2}+mx+n=x^{2}-2x-3$$

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

$$mx+n=x^{2}-2x-3-x^{2}$$

Pahekotia te x^{2} me -x^{2}, ka 0.

$$mx+n=-2x-3$$

Tangohia te mx mai i ngā taha e rua.

$$n=-2x-3-mx$$