Whakaoti i te f(x)=x^2-7x+10

$$f ( x ) = x ^ { 2 } - 7 x + 10$$

Tauwehe

$$\left(x-5\right)\left(x-2\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+10. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=1\times 10=10$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 10.

$$-1,-10 -2,-5$$

Tātaihia te tapeke mō ia takirua.

$$-1-10=-11 -2-5=-7$$

Ko te otinga te takirua ka hoatu i te tapeke -7.

$$a=-5 b=-2$$

Tuhia anō te x^{2}-7x+10 hei \left(x^{2}-5x\right)+\left(-2x+10\right).

$$\left(x^{2}-5x\right)+\left(-2x+10\right)$$

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

$$x\left(x-5\right)-2\left(x-5\right)$$

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

$$\left(x-5\right)\left(x-2\right)$$

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.

$$x^{2}-7x+10=0$$

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.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 10}}{2}$$

Pūrua -7.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\times 10}}{2}$$

Whakareatia -4 ki te 10.

$$x=\frac{-\left(-7\right)±\sqrt{49-40}}{2}$$

Tāpiri 49 ki te -40.

$$x=\frac{-\left(-7\right)±\sqrt{9}}{2}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{-\left(-7\right)±3}{2}$$

Ko te tauaro o -7 ko 7.

$$x=\frac{7±3}{2}$$

Nā, me whakaoti te whārite x=\frac{7±3}{2} ina he tāpiri te ±. Tāpiri 7 ki te 3.

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

Whakawehe 10 ki te 2.

$$x=5$$

Nā, me whakaoti te whārite x=\frac{7±3}{2} ina he tango te ±. Tango 3 mai i 7.

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

Whakawehe 4 ki te 2.

$$x=2$$

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 5 mō te x_{1} me te 2 mō te x_{2}.

$$x^{2}-7x+10=\left(x-5\right)\left(x-2\right)$$

Aromātai

$$\left(x-5\right)\left(x-2\right)$$