Whakaoti i te x^2+14x+24

$$x ^ { 2 } + 14 x + 24$$

Tauwehe

$$\left(x+2\right)\left(x+12\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=14 ab=1\times 24=24$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 24.

$$1,24 2,12 3,8 4,6$$

Tātaihia te tapeke mō ia takirua.

$$1+24=25 2+12=14 3+8=11 4+6=10$$

Ko te otinga te takirua ka hoatu i te tapeke 14.

$$a=2 b=12$$

Tuhia anō te x^{2}+14x+24 hei \left(x^{2}+2x\right)+\left(12x+24\right).

$$\left(x^{2}+2x\right)+\left(12x+24\right)$$

Tauwehea te x i te tuatahi me te 12 i te rōpū tuarua.

$$x\left(x+2\right)+12\left(x+2\right)$$

Whakatauwehea atu te kīanga pātahi x+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x+2\right)\left(x+12\right)$$

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.

$$x^{2}+14x+24=0$$

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.

$$x=\frac{-14±\sqrt{14^{2}-4\times 24}}{2}$$

Pūrua 14.

$$x=\frac{-14±\sqrt{196-4\times 24}}{2}$$

Whakareatia -4 ki te 24.

$$x=\frac{-14±\sqrt{196-96}}{2}$$

Tāpiri 196 ki te -96.

$$x=\frac{-14±\sqrt{100}}{2}$$

Tuhia te pūtakerua o te 100.

$$x=\frac{-14±10}{2}$$

Nā, me whakaoti te whārite x=\frac{-14±10}{2} ina he tāpiri te ±. Tāpiri -14 ki te 10.

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

Whakawehe -4 ki te 2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-14±10}{2} ina he tango te ±. Tango 10 mai i -14.

$$x=-\frac{24}{2}$$

Whakawehe -24 ki te 2.

$$x=-12$$

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 -12 mō te x_{2}.

$$x^{2}+14x+24=\left(x-\left(-2\right)\right)\left(x-\left(-12\right)\right)$$

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

$$x^{2}+14x+24=\left(x+2\right)\left(x+12\right)$$

Aromātai

$$\left(x+2\right)\left(x+12\right)$$