Whakaoti i te x^2+11x+30

$$x ^ { 2 } + 11 x + 30$$

Tauwehe

$$\left(x+5\right)\left(x+6\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=11 ab=1\times 30=30$$

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 30.

$$1,30 2,15 3,10 5,6$$

Tātaihia te tapeke mō ia takirua.

$$1+30=31 2+15=17 3+10=13 5+6=11$$

Ko te otinga te takirua ka hoatu i te tapeke 11.

$$a=5 b=6$$

Tuhia anō te x^{2}+11x+30 hei \left(x^{2}+5x\right)+\left(6x+30\right).

$$\left(x^{2}+5x\right)+\left(6x+30\right)$$

Tauwehea te x i te tuatahi me te 6 i te rōpū tuarua.

$$x\left(x+5\right)+6\left(x+5\right)$$

Whakatauwehea atu te kīanga pātahi x+5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x+5\right)\left(x+6\right)$$

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.

$$x^{2}+11x+30=0$$

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.

$$x=\frac{-11±\sqrt{11^{2}-4\times 30}}{2}$$

Pūrua 11.

$$x=\frac{-11±\sqrt{121-4\times 30}}{2}$$

Whakareatia -4 ki te 30.

$$x=\frac{-11±\sqrt{121-120}}{2}$$

Tāpiri 121 ki te -120.

$$x=\frac{-11±\sqrt{1}}{2}$$

Tuhia te pūtakerua o te 1.

$$x=\frac{-11±1}{2}$$

Nā, me whakaoti te whārite x=\frac{-11±1}{2} ina he tāpiri te ±. Tāpiri -11 ki te 1.

$$x=-\frac{10}{2}$$

Whakawehe -10 ki te 2.

$$x=-5$$

Nā, me whakaoti te whārite x=\frac{-11±1}{2} ina he tango te ±. Tango 1 mai i -11.

$$x=-\frac{12}{2}$$

Whakawehe -12 ki te 2.

$$x=-6$$

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 -5 mō te x_{1} me te -6 mō te x_{2}.

$$x^{2}+11x+30=\left(x-\left(-5\right)\right)\left(x-\left(-6\right)\right)$$

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

$$x^{2}+11x+30=\left(x+5\right)\left(x+6\right)$$

Aromātai

$$\left(x+5\right)\left(x+6\right)$$