Whakaoti i te 12-5x-2x^2

$$12 - 5 x - 2 x ^ { 2 }$$

Tauwehe

$$-\left(2x-3\right)\left(x+4\right)$$

Ngā Upane Otinga

Hurinahatia te pūrau ki te āhua tānga ngahuru. Whakaraupapahia ngā kīanga tau mai i te pū teitei rawa ki te mea iti rawa.

$$-2x^{2}-5x+12$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -2x^{2}+ax+bx+12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=-2\times 12=-24$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. 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.

$$1-24=-23 2-12=-10 3-8=-5 4-6=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -5.

$$a=3 b=-8$$

Tuhia anō te -2x^{2}-5x+12 hei \left(-2x^{2}+3x\right)+\left(-8x+12\right).

$$\left(-2x^{2}+3x\right)+\left(-8x+12\right)$$

Tauwehea te -x i te tuatahi me te -4 i te rōpū tuarua.

$$-x\left(2x-3\right)-4\left(2x-3\right)$$

Whakatauwehea atu te kīanga pātahi 2x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2x-3\right)\left(-x-4\right)$$

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.

$$-2x^{2}-5x+12=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-2\right)\times 12}}{2\left(-2\right)}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-2\right)\times 12}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-\left(-5\right)±\sqrt{25+8\times 12}}{2\left(-2\right)}$$

Whakareatia 8 ki te 12.

$$x=\frac{-\left(-5\right)±\sqrt{25+96}}{2\left(-2\right)}$$

Tāpiri 25 ki te 96.

$$x=\frac{-\left(-5\right)±\sqrt{121}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-\left(-5\right)±11}{2\left(-2\right)}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±11}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{5±11}{-4}$$

Nā, me whakaoti te whārite x=\frac{5±11}{-4} ina he tāpiri te ±. Tāpiri 5 ki te 11.

$$x=\frac{16}{-4}$$

Whakawehe 16 ki te -4.

$$x=-4$$

Nā, me whakaoti te whārite x=\frac{5±11}{-4} ina he tango te ±. Tango 11 mai i 5.

$$x=-\frac{6}{-4}$$

Whakahekea te hautanga \frac{-6}{-4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{3}{2}$$

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 -4 mō te x_{1} me te \frac{3}{2} mō te x_{2}.

$$-2x^{2}-5x+12=-2\left(x-\left(-4\right)\right)\left(x-\frac{3}{2}\right)$$

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

$$-2x^{2}-5x+12=-2\left(x+4\right)\left(x-\frac{3}{2}\right)$$

Tango \frac{3}{2} mai i x mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$-2x^{2}-5x+12=-2\left(x+4\right)\times \frac{-2x+3}{-2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te -2 me te 2.

$$-2x^{2}-5x+12=\left(x+4\right)\left(-2x+3\right)$$

Aromātai

$$-\left(2x-3\right)\left(x+4\right)$$