Whakaoti i te f(7)=x^2+9x+14

$$f ( 7 ) = x ^ { 2 } + 9 x + 14$$

Tauwehe

$$\left(x+2\right)\left(x+7\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+14. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=9 ab=1\times 14=14$$

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 14.

$$1,14 2,7$$

Tātaihia te tapeke mō ia takirua.

$$1+14=15 2+7=9$$

Ko te otinga te takirua ka hoatu i te tapeke 9.

$$a=2 b=7$$

Tuhia anō te x^{2}+9x+14 hei \left(x^{2}+2x\right)+\left(7x+14\right).

$$\left(x^{2}+2x\right)+\left(7x+14\right)$$

Tauwehea te x i te tuatahi me te 7 i te rōpū tuarua.

$$x\left(x+2\right)+7\left(x+2\right)$$

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

$$\left(x+2\right)\left(x+7\right)$$

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.

$$x^{2}+9x+14=0$$

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.

$$x=\frac{-9±\sqrt{9^{2}-4\times 14}}{2}$$

Pūrua 9.

$$x=\frac{-9±\sqrt{81-4\times 14}}{2}$$

Whakareatia -4 ki te 14.

$$x=\frac{-9±\sqrt{81-56}}{2}$$

Tāpiri 81 ki te -56.

$$x=\frac{-9±\sqrt{25}}{2}$$

Tuhia te pūtakerua o te 25.

$$x=\frac{-9±5}{2}$$

Nā, me whakaoti te whārite x=\frac{-9±5}{2} ina he tāpiri te ±. Tāpiri -9 ki te 5.

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

Whakawehe -4 ki te 2.

$$x=-2$$

Nā, me whakaoti te whārite x=\frac{-9±5}{2} ina he tango te ±. Tango 5 mai i -9.

$$x=-\frac{14}{2}$$

Whakawehe -14 ki te 2.

$$x=-7$$

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 -7 mō te x_{2}.

$$x^{2}+9x+14=\left(x-\left(-2\right)\right)\left(x-\left(-7\right)\right)$$

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

$$x^{2}+9x+14=\left(x+2\right)\left(x+7\right)$$

Aromātai

$$\left(x+2\right)\left(x+7\right)$$