Whakaoti i te m^2-13m-30?

$$m ^ { 2 } - 13 m - 30 ?$$

Tauwehe

$$\left(m-15\right)\left(m+2\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei m^{2}+am+bm-30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=1\left(-30\right)=-30$$

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 -13.

$$a=-15 b=2$$

Tuhia anō te m^{2}-13m-30 hei \left(m^{2}-15m\right)+\left(2m-30\right).

$$\left(m^{2}-15m\right)+\left(2m-30\right)$$

Tauwehea te m i te tuatahi me te 2 i te rōpū tuarua.

$$m\left(m-15\right)+2\left(m-15\right)$$

Whakatauwehea atu te kīanga pātahi m-15 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-15\right)\left(m+2\right)$$

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.

$$m^{2}-13m-30=0$$

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.

$$m=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\left(-30\right)}}{2}$$

Pūrua -13.

$$m=\frac{-\left(-13\right)±\sqrt{169-4\left(-30\right)}}{2}$$

Whakareatia -4 ki te -30.

$$m=\frac{-\left(-13\right)±\sqrt{169+120}}{2}$$

Tāpiri 169 ki te 120.

$$m=\frac{-\left(-13\right)±\sqrt{289}}{2}$$

Tuhia te pūtakerua o te 289.

$$m=\frac{-\left(-13\right)±17}{2}$$

Ko te tauaro o -13 ko 13.

$$m=\frac{13±17}{2}$$

Nā, me whakaoti te whārite m=\frac{13±17}{2} ina he tāpiri te ±. Tāpiri 13 ki te 17.

$$m=\frac{30}{2}$$

Whakawehe 30 ki te 2.

$$m=15$$

Nā, me whakaoti te whārite m=\frac{13±17}{2} ina he tango te ±. Tango 17 mai i 13.

$$m=-\frac{4}{2}$$

Whakawehe -4 ki te 2.

$$m=-2$$

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 15 mō te x_{1} me te -2 mō te x_{2}.

$$m^{2}-13m-30=\left(m-15\right)\left(m-\left(-2\right)\right)$$

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

$$m^{2}-13m-30=\left(m-15\right)\left(m+2\right)$$

Aromātai

$$\left(m-15\right)\left(m+2\right)$$