Whakaoti i te 6s^2+11s-35

$$6 s ^ { 2 } + 11 s - 35$$

Tauwehe

$$\left(3s-5\right)\left(2s+7\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6s^{2}+as+bs-35. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=11 ab=6\left(-35\right)=-210$$

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 -210.

$$-1,210 -2,105 -3,70 -5,42 -6,35 -7,30 -10,21 -14,15$$

Tātaihia te tapeke mō ia takirua.

$$-1+210=209 -2+105=103 -3+70=67 -5+42=37 -6+35=29 -7+30=23 -10+21=11 -14+15=1$$

Ko te otinga te takirua ka hoatu i te tapeke 11.

$$a=-10 b=21$$

Tuhia anō te 6s^{2}+11s-35 hei \left(6s^{2}-10s\right)+\left(21s-35\right).

$$\left(6s^{2}-10s\right)+\left(21s-35\right)$$

Tauwehea te 2s i te tuatahi me te 7 i te rōpū tuarua.

$$2s\left(3s-5\right)+7\left(3s-5\right)$$

Whakatauwehea atu te kīanga pātahi 3s-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3s-5\right)\left(2s+7\right)$$

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.

$$6s^{2}+11s-35=0$$

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.

$$s=\frac{-11±\sqrt{11^{2}-4\times 6\left(-35\right)}}{2\times 6}$$

Pūrua 11.

$$s=\frac{-11±\sqrt{121-4\times 6\left(-35\right)}}{2\times 6}$$

Whakareatia -4 ki te 6.

$$s=\frac{-11±\sqrt{121-24\left(-35\right)}}{2\times 6}$$

Whakareatia -24 ki te -35.

$$s=\frac{-11±\sqrt{121+840}}{2\times 6}$$

Tāpiri 121 ki te 840.

$$s=\frac{-11±\sqrt{961}}{2\times 6}$$

Tuhia te pūtakerua o te 961.

$$s=\frac{-11±31}{2\times 6}$$

Whakareatia 2 ki te 6.

$$s=\frac{-11±31}{12}$$

Nā, me whakaoti te whārite s=\frac{-11±31}{12} ina he tāpiri te ±. Tāpiri -11 ki te 31.

$$s=\frac{20}{12}$$

Whakahekea te hautanga \frac{20}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

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

Nā, me whakaoti te whārite s=\frac{-11±31}{12} ina he tango te ±. Tango 31 mai i -11.

$$s=-\frac{42}{12}$$

Whakahekea te hautanga \frac{-42}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$s=-\frac{7}{2}$$

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 \frac{5}{3} mō te x_{1} me te -\frac{7}{2} mō te x_{2}.

$$6s^{2}+11s-35=6\left(s-\frac{5}{3}\right)\left(s-\left(-\frac{7}{2}\right)\right)$$

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

$$6s^{2}+11s-35=6\left(s-\frac{5}{3}\right)\left(s+\frac{7}{2}\right)$$

Tango \frac{5}{3} mai i s 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.

$$6s^{2}+11s-35=6\times \frac{3s-5}{3}\left(s+\frac{7}{2}\right)$$

Tāpiri \frac{7}{2} 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.

$$6s^{2}+11s-35=6\times \frac{3s-5}{3}\times \frac{2s+7}{2}$$

Whakareatia \frac{3s-5}{3} ki te \frac{2s+7}{2} 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.

$$6s^{2}+11s-35=6\times \frac{\left(3s-5\right)\left(2s+7\right)}{3\times 2}$$

Whakareatia 3 ki te 2.

$$6s^{2}+11s-35=6\times \frac{\left(3s-5\right)\left(2s+7\right)}{6}$$

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

$$6s^{2}+11s-35=\left(3s-5\right)\left(2s+7\right)$$

Aromātai

$$\left(3s-5\right)\left(2s+7\right)$$