Whakaoti i te -a^2+a+6=

$$- a ^ { 2 } + a + 6 =$$

Tauwehe

$$-\left(a-3\right)\left(a+2\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -a^{2}+pa+qa+6. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=1 pq=-6=-6$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōrunga te p+q, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -6.

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

Tātaihia te tapeke mō ia takirua.

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

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$p=3 q=-2$$

Tuhia anō te -a^{2}+a+6 hei \left(-a^{2}+3a\right)+\left(-2a+6\right).

$$\left(-a^{2}+3a\right)+\left(-2a+6\right)$$

Tauwehea te -a i te tuatahi me te -2 i te rōpū tuarua.

$$-a\left(a-3\right)-2\left(a-3\right)$$

Whakatauwehea atu te kīanga pātahi a-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(a-3\right)\left(-a-2\right)$$

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.

$$-a^{2}+a+6=0$$

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.

$$a=\frac{-1±\sqrt{1^{2}-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

Pūrua 1.

$$a=\frac{-1±\sqrt{1-4\left(-1\right)\times 6}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$a=\frac{-1±\sqrt{1+4\times 6}}{2\left(-1\right)}$$

Whakareatia 4 ki te 6.

$$a=\frac{-1±\sqrt{1+24}}{2\left(-1\right)}$$

Tāpiri 1 ki te 24.

$$a=\frac{-1±\sqrt{25}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 25.

$$a=\frac{-1±5}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$a=\frac{-1±5}{-2}$$

Nā, me whakaoti te whārite a=\frac{-1±5}{-2} ina he tāpiri te ±. Tāpiri -1 ki te 5.

$$a=\frac{4}{-2}$$

Whakawehe 4 ki te -2.

$$a=-2$$

Nā, me whakaoti te whārite a=\frac{-1±5}{-2} ina he tango te ±. Tango 5 mai i -1.

$$a=-\frac{6}{-2}$$

Whakawehe -6 ki te -2.

$$a=3$$

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 -2 mō te x_{1} me te 3 mō te x_{2}.

$$-a^{2}+a+6=-\left(a-\left(-2\right)\right)\left(a-3\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$-a^{2}+a+6=-\left(a+2\right)\left(a-3\right)$$

Aromātai

$$-\left(a-3\right)\left(a+2\right)$$