Whakaoti i te T(x)=-x^2+3x-2

$$T ( x ) = - x ^ { 2 } + 3 x - 2$$

Tauwehe

$$\left(1-x\right)\left(x-2\right)$$

Ngā Upane Otinga

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

$$a+b=3 ab=-\left(-2\right)=2$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=2 b=1$$

Tuhia anō te -x^{2}+3x-2 hei \left(-x^{2}+2x\right)+\left(x-2\right).

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

Whakatauwehea atu -x i te -x^{2}+2x.

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

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

$$\left(x-2\right)\left(-x+1\right)$$

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.

$$-x^{2}+3x-2=0$$

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.

$$x=\frac{-3±\sqrt{3^{2}-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-3±\sqrt{9+4\left(-2\right)}}{2\left(-1\right)}$$

Whakareatia 4 ki te -2.

$$x=\frac{-3±\sqrt{9-8}}{2\left(-1\right)}$$

Tāpiri 9 ki te -8.

$$x=\frac{-3±\sqrt{1}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 1.

$$x=\frac{-3±1}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-3±1}{-2}$$

Nā, me whakaoti te whārite x=\frac{-3±1}{-2} ina he tāpiri te ±. Tāpiri -3 ki te 1.

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

Whakawehe -2 ki te -2.

$$x=1$$

Nā, me whakaoti te whārite x=\frac{-3±1}{-2} ina he tango te ±. Tango 1 mai i -3.

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

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 1 mō te x_{1} me te 2 mō te x_{2}.

$$-x^{2}+3x-2=-\left(x-1\right)\left(x-2\right)$$

Aromātai

$$\left(1-x\right)\left(x-2\right)$$