Whakaoti i te x^2+5x-24

$${ x }^{ 2 } +5x-24$$

Tauwehe

$$\left(x-3\right)\left(x+8\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=1\left(-24\right)=-24$$

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 -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 x^{2}+5x-24 hei \left(x^{2}-3x\right)+\left(8x-24\right).

$$\left(x^{2}-3x\right)+\left(8x-24\right)$$

Tauwehea te x i te tuatahi me te 8 i te rōpū tuarua.

$$x\left(x-3\right)+8\left(x-3\right)$$

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

$$\left(x-3\right)\left(x+8\right)$$

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.

$$x^{2}+5x-24=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-24\right)}}{2}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-24\right)}}{2}$$

Whakareatia -4 ki te -24.

$$x=\frac{-5±\sqrt{25+96}}{2}$$

Tāpiri 25 ki te 96.

$$x=\frac{-5±\sqrt{121}}{2}$$

Tuhia te pūtakerua o te 121.

$$x=\frac{-5±11}{2}$$

Nā, me whakaoti te whārite x=\frac{-5±11}{2} ina he tāpiri te ±. Tāpiri -5 ki te 11.

$$x=\frac{6}{2}$$

Whakawehe 6 ki te 2.

$$x=3$$

Nā, me whakaoti te whārite x=\frac{-5±11}{2} ina he tango te ±. Tango 11 mai i -5.

$$x=-\frac{16}{2}$$

Whakawehe -16 ki te 2.

$$x=-8$$

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 3 mō te x_{1} me te -8 mō te x_{2}.

$$x^{2}+5x-24=\left(x-3\right)\left(x-\left(-8\right)\right)$$

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

$$x^{2}+5x-24=\left(x-3\right)\left(x+8\right)$$

Aromātai

$$\left(x-3\right)\left(x+8\right)$$