Whakaoti i te 2k^2-14k-60

$$2 k ^ { 2 } - 14 k - 60$$

Tauwehe

$$2\left(k-10\right)\left(k+3\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(k^{2}-7k-30\right)$$

Whakaarohia te k^{2}-7k-30. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei k^{2}+ak+bk-30. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=1\left(-30\right)=-30$$

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 -7.

$$a=-10 b=3$$

Tuhia anō te k^{2}-7k-30 hei \left(k^{2}-10k\right)+\left(3k-30\right).

$$\left(k^{2}-10k\right)+\left(3k-30\right)$$

Tauwehea te k i te tuatahi me te 3 i te rōpū tuarua.

$$k\left(k-10\right)+3\left(k-10\right)$$

Whakatauwehea atu te kīanga pātahi k-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(k-10\right)\left(k+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(k-10\right)\left(k+3\right)$$

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.

$$2k^{2}-14k-60=0$$

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.

$$k=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 2\left(-60\right)}}{2\times 2}$$

Pūrua -14.

$$k=\frac{-\left(-14\right)±\sqrt{196-4\times 2\left(-60\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$k=\frac{-\left(-14\right)±\sqrt{196-8\left(-60\right)}}{2\times 2}$$

Whakareatia -8 ki te -60.

$$k=\frac{-\left(-14\right)±\sqrt{196+480}}{2\times 2}$$

Tāpiri 196 ki te 480.

$$k=\frac{-\left(-14\right)±\sqrt{676}}{2\times 2}$$

Tuhia te pūtakerua o te 676.

$$k=\frac{-\left(-14\right)±26}{2\times 2}$$

Ko te tauaro o -14 ko 14.

$$k=\frac{14±26}{2\times 2}$$

Whakareatia 2 ki te 2.

$$k=\frac{14±26}{4}$$

Nā, me whakaoti te whārite k=\frac{14±26}{4} ina he tāpiri te ±. Tāpiri 14 ki te 26.

$$k=\frac{40}{4}$$

Whakawehe 40 ki te 4.

$$k=10$$

Nā, me whakaoti te whārite k=\frac{14±26}{4} ina he tango te ±. Tango 26 mai i 14.

$$k=-\frac{12}{4}$$

Whakawehe -12 ki te 4.

$$k=-3$$

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 10 mō te x_{1} me te -3 mō te x_{2}.

$$2k^{2}-14k-60=2\left(k-10\right)\left(k-\left(-3\right)\right)$$

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

$$2k^{2}-14k-60=2\left(k-10\right)\left(k+3\right)$$

Aromātai

$$2\left(k-10\right)\left(k+3\right)$$