Whakaoti i te 5s^2-7s-6

$$5 s ^ { 2 } - 7 s - 6$$

Tauwehe

$$\left(s-2\right)\left(5s+3\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 5s^{2}+as+bs-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=5\left(-6\right)=-30$$

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 -30.

$$1,-30 2,-15 3,-10 5,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -7.

$$a=-10 b=3$$

Tuhia anō te 5s^{2}-7s-6 hei \left(5s^{2}-10s\right)+\left(3s-6\right).

$$\left(5s^{2}-10s\right)+\left(3s-6\right)$$

Tauwehea te 5s i te tuatahi me te 3 i te rōpū tuarua.

$$5s\left(s-2\right)+3\left(s-2\right)$$

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

$$\left(s-2\right)\left(5s+3\right)$$

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.

$$5s^{2}-7s-6=0$$

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.

$$s=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\times 5\left(-6\right)}}{2\times 5}$$

Pūrua -7.

$$s=\frac{-\left(-7\right)±\sqrt{49-4\times 5\left(-6\right)}}{2\times 5}$$

Whakareatia -4 ki te 5.

$$s=\frac{-\left(-7\right)±\sqrt{49-20\left(-6\right)}}{2\times 5}$$

Whakareatia -20 ki te -6.

$$s=\frac{-\left(-7\right)±\sqrt{49+120}}{2\times 5}$$

Tāpiri 49 ki te 120.

$$s=\frac{-\left(-7\right)±\sqrt{169}}{2\times 5}$$

Tuhia te pūtakerua o te 169.

$$s=\frac{-\left(-7\right)±13}{2\times 5}$$

Ko te tauaro o -7 ko 7.

$$s=\frac{7±13}{2\times 5}$$

Whakareatia 2 ki te 5.

$$s=\frac{7±13}{10}$$

Nā, me whakaoti te whārite s=\frac{7±13}{10} ina he tāpiri te ±. Tāpiri 7 ki te 13.

$$s=\frac{20}{10}$$

Whakawehe 20 ki te 10.

$$s=2$$

Nā, me whakaoti te whārite s=\frac{7±13}{10} ina he tango te ±. Tango 13 mai i 7.

$$s=-\frac{6}{10}$$

Whakahekea te hautanga \frac{-6}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$s=-\frac{3}{5}$$

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 2 mō te x_{1} me te -\frac{3}{5} mō te x_{2}.

$$5s^{2}-7s-6=5\left(s-2\right)\left(s-\left(-\frac{3}{5}\right)\right)$$

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

$$5s^{2}-7s-6=5\left(s-2\right)\left(s+\frac{3}{5}\right)$$

Tāpiri \frac{3}{5} ki te s 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.

$$5s^{2}-7s-6=5\left(s-2\right)\times \frac{5s+3}{5}$$

Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 5 me te 5.

$$5s^{2}-7s-6=\left(s-2\right)\left(5s+3\right)$$

Aromātai

$$\left(s-2\right)\left(5s+3\right)$$