Whakaoti i te a^2-4a-12

$$a ^ { 2 } - 4 a - 12$$

Tauwehe

$$\left(a-6\right)\left(a+2\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei a^{2}+pa+qa-12. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=-4 pq=1\left(-12\right)=-12$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōraro te p+q, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$1,-12 2,-6 3,-4$$

Tātaihia te tapeke mō ia takirua.

$$1-12=-11 2-6=-4 3-4=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -4.

$$p=-6 q=2$$

Tuhia anō te a^{2}-4a-12 hei \left(a^{2}-6a\right)+\left(2a-12\right).

$$\left(a^{2}-6a\right)+\left(2a-12\right)$$

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

$$a\left(a-6\right)+2\left(a-6\right)$$

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

$$\left(a-6\right)\left(a+2\right)$$

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.

$$a^{2}-4a-12=0$$

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.

$$a=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-12\right)}}{2}$$

Pūrua -4.

$$a=\frac{-\left(-4\right)±\sqrt{16-4\left(-12\right)}}{2}$$

Whakareatia -4 ki te -12.

$$a=\frac{-\left(-4\right)±\sqrt{16+48}}{2}$$

Tāpiri 16 ki te 48.

$$a=\frac{-\left(-4\right)±\sqrt{64}}{2}$$

Tuhia te pūtakerua o te 64.

$$a=\frac{-\left(-4\right)±8}{2}$$

Ko te tauaro o -4 ko 4.

$$a=\frac{4±8}{2}$$

Nā, me whakaoti te whārite a=\frac{4±8}{2} ina he tāpiri te ±. Tāpiri 4 ki te 8.

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

Whakawehe 12 ki te 2.

$$a=6$$

Nā, me whakaoti te whārite a=\frac{4±8}{2} ina he tango te ±. Tango 8 mai i 4.

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

Whakawehe -4 ki te 2.

$$a=-2$$

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 -2 mō te x_{2}.

$$a^{2}-4a-12=\left(a-6\right)\left(a-\left(-2\right)\right)$$

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

$$a^{2}-4a-12=\left(a-6\right)\left(a+2\right)$$

Aromātai

$$\left(a-6\right)\left(a+2\right)$$