Whakaoti i te z^2-7z+6

$$z ^ { 2 } - 7 z + 6$$

Tauwehe

$$\left(z-6\right)\left(z-1\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei z^{2}+az+bz+6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=1\times 6=6$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 6.

$$-1,-6 -2,-3$$

Tātaihia te tapeke mō ia takirua.

$$-1-6=-7 -2-3=-5$$

Ko te otinga te takirua ka hoatu i te tapeke -7.

$$a=-6 b=-1$$

Tuhia anō te z^{2}-7z+6 hei \left(z^{2}-6z\right)+\left(-z+6\right).

$$\left(z^{2}-6z\right)+\left(-z+6\right)$$

Tauwehea te z i te tuatahi me te -1 i te rōpū tuarua.

$$z\left(z-6\right)-\left(z-6\right)$$

Whakatauwehea atu te kīanga pātahi z-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(z-6\right)\left(z-1\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$z^{2}-7z+6=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$z=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 6}}{2}$$

Pūrua -7.

$$z=\frac{-\left(-7\right)±\sqrt{49-4\times 6}}{2}$$

Whakareatia -4 ki te 6.

$$z=\frac{-\left(-7\right)±\sqrt{49-24}}{2}$$

Tāpiri 49 ki te -24.

$$z=\frac{-\left(-7\right)±\sqrt{25}}{2}$$

Tuhia te pūtakerua o te 25.

$$z=\frac{-\left(-7\right)±5}{2}$$

Ko te tauaro o -7 ko 7.

$$z=\frac{7±5}{2}$$

Nā, me whakaoti te whārite z=\frac{7±5}{2} ina he tāpiri te ±. Tāpiri 7 ki te 5.

$$z=\frac{12}{2}$$

Whakawehe 12 ki te 2.

$$z=6$$

Nā, me whakaoti te whārite z=\frac{7±5}{2} ina he tango te ±. Tango 5 mai i 7.

$$z=\frac{2}{2}$$

Whakawehe 2 ki te 2.

$$z=1$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 6 mō te x_{1} me te 1 mō te x_{2}.

$$z^{2}-7z+6=\left(z-6\right)\left(z-1\right)$$

Aromātai

$$\left(z-6\right)\left(z-1\right)$$