Whakaoti i te 6x^2-25x+4

$$6 x ^ { 2 } - 25 x + 4$$

Tauwehe

$$\left(x-4\right)\left(6x-1\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6x^{2}+ax+bx+4. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-25 ab=6\times 4=24$$

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 24.

$$-1,-24 -2,-12 -3,-8 -4,-6$$

Tātaihia te tapeke mō ia takirua.

$$-1-24=-25 -2-12=-14 -3-8=-11 -4-6=-10$$

Ko te otinga te takirua ka hoatu i te tapeke -25.

$$a=-24 b=-1$$

Tuhia anō te 6x^{2}-25x+4 hei \left(6x^{2}-24x\right)+\left(-x+4\right).

$$\left(6x^{2}-24x\right)+\left(-x+4\right)$$

Tauwehea te 6x i te tuatahi me te -1 i te rōpū tuarua.

$$6x\left(x-4\right)-\left(x-4\right)$$

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

$$\left(x-4\right)\left(6x-1\right)$$

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.

$$6x^{2}-25x+4=0$$

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.

$$x=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}-4\times 6\times 4}}{2\times 6}$$

Pūrua -25.

$$x=\frac{-\left(-25\right)±\sqrt{625-4\times 6\times 4}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$x=\frac{-\left(-25\right)±\sqrt{625-24\times 4}}{2\times 6}$$

Whakareatia -24 ki te 4.

$$x=\frac{-\left(-25\right)±\sqrt{625-96}}{2\times 6}$$

Tāpiri 625 ki te -96.

$$x=\frac{-\left(-25\right)±\sqrt{529}}{2\times 6}$$

Tuhia te pūtakerua o te 529.

$$x=\frac{-\left(-25\right)±23}{2\times 6}$$

Ko te tauaro o -25 ko 25.

$$x=\frac{25±23}{2\times 6}$$

Whakareatia 2 ki te 6.

$$x=\frac{25±23}{12}$$

Nā, me whakaoti te whārite x=\frac{25±23}{12} ina he tāpiri te ±. Tāpiri 25 ki te 23.

$$x=\frac{48}{12}$$

Whakawehe 48 ki te 12.

$$x=4$$

Nā, me whakaoti te whārite x=\frac{25±23}{12} ina he tango te ±. Tango 23 mai i 25.

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

Whakahekea te hautanga \frac{2}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{1}{6}$$

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 4 mō te x_{1} me te \frac{1}{6} mō te x_{2}.

$$6x^{2}-25x+4=6\left(x-4\right)\left(x-\frac{1}{6}\right)$$

Tango \frac{1}{6} 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.

$$6x^{2}-25x+4=6\left(x-4\right)\times \frac{6x-1}{6}$$

Whakakorea atu te tauwehe pūnoa nui rawa 6 i roto i te 6 me te 6.

$$6x^{2}-25x+4=\left(x-4\right)\left(6x-1\right)$$

Aromātai

$$\left(x-4\right)\left(6x-1\right)$$