Whakaoti i te -12x^2+x+6

$$- 12 x ^ { 2 } + x + 6$$

Tauwehe

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

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -12x^{2}+ax+bx+6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=-12\times 6=-72$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -72.

$$-1,72 -2,36 -3,24 -4,18 -6,12 -8,9$$

Tātaihia te tapeke mō ia takirua.

$$-1+72=71 -2+36=34 -3+24=21 -4+18=14 -6+12=6 -8+9=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=9 b=-8$$

Tuhia anō te -12x^{2}+x+6 hei \left(-12x^{2}+9x\right)+\left(-8x+6\right).

$$\left(-12x^{2}+9x\right)+\left(-8x+6\right)$$

Tauwehea te 3x i te tuatahi me te 2 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi -4x+3 mā te whakamahi i te āhuatanga tātai tohatoha.

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

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.

$$-12x^{2}+x+6=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-12\right)\times 6}}{2\left(-12\right)}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\left(-12\right)\times 6}}{2\left(-12\right)}$$

Whakareatia -4 ki te -12.

$$x=\frac{-1±\sqrt{1+48\times 6}}{2\left(-12\right)}$$

Whakareatia 48 ki te 6.

$$x=\frac{-1±\sqrt{1+288}}{2\left(-12\right)}$$

Tāpiri 1 ki te 288.

$$x=\frac{-1±\sqrt{289}}{2\left(-12\right)}$$

Tuhia te pūtakerua o te 289.

$$x=\frac{-1±17}{2\left(-12\right)}$$

Whakareatia 2 ki te -12.

$$x=\frac{-1±17}{-24}$$

Nā, me whakaoti te whārite x=\frac{-1±17}{-24} ina he tāpiri te ±. Tāpiri -1 ki te 17.

$$x=\frac{16}{-24}$$

Whakahekea te hautanga \frac{16}{-24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

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

Nā, me whakaoti te whārite x=\frac{-1±17}{-24} ina he tango te ±. Tango 17 mai i -1.

$$x=-\frac{18}{-24}$$

Whakahekea te hautanga \frac{-18}{-24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=\frac{3}{4}$$

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

$$-12x^{2}+x+6=-12\left(x-\left(-\frac{2}{3}\right)\right)\left(x-\frac{3}{4}\right)$$

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

$$-12x^{2}+x+6=-12\left(x+\frac{2}{3}\right)\left(x-\frac{3}{4}\right)$$

Tāpiri \frac{2}{3} ki te x mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$-12x^{2}+x+6=-12\times \frac{-3x-2}{-3}\left(x-\frac{3}{4}\right)$$

Tango \frac{3}{4} 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.

$$-12x^{2}+x+6=-12\times \frac{-3x-2}{-3}\times \frac{-4x+3}{-4}$$

Whakareatia \frac{-3x-2}{-3} ki te \frac{-4x+3}{-4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$-12x^{2}+x+6=-12\times \frac{\left(-3x-2\right)\left(-4x+3\right)}{-3\left(-4\right)}$$

Whakareatia -3 ki te -4.

$$-12x^{2}+x+6=-12\times \frac{\left(-3x-2\right)\left(-4x+3\right)}{12}$$

Whakakorea atu te tauwehe pūnoa nui rawa 12 i roto i te -12 me te 12.

$$-12x^{2}+x+6=-\left(-3x-2\right)\left(-4x+3\right)$$

Aromātai

$$6+x-12x^{2}$$