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a+b=-2 ab=1\left(-24\right)=-24
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei n^{2}+an+bn-24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,-24 2,-12 3,-8 4,-6
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 -24.
1-24=-23 2-12=-10 3-8=-5 4-6=-2
Tātaihia te tapeke mō ia takirua.
a=-6 b=4
Ko te otinga te takirua ka hoatu i te tapeke -2.
\left(n^{2}-6n\right)+\left(4n-24\right)
Tuhia anō te n^{2}-2n-24 hei \left(n^{2}-6n\right)+\left(4n-24\right).
n\left(n-6\right)+4\left(n-6\right)
Tauwehea te n i te tuatahi me te 4 i te rōpū tuarua.
\left(n-6\right)\left(n+4\right)
Whakatauwehea atu te kīanga pātahi n-6 mā te whakamahi i te āhuatanga tātai tohatoha.
n^{2}-2n-24=0
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.
n=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-24\right)}}{2}
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.
n=\frac{-\left(-2\right)±\sqrt{4-4\left(-24\right)}}{2}
Pūrua -2.
n=\frac{-\left(-2\right)±\sqrt{4+96}}{2}
Whakareatia -4 ki te -24.
n=\frac{-\left(-2\right)±\sqrt{100}}{2}
Tāpiri 4 ki te 96.
n=\frac{-\left(-2\right)±10}{2}
Tuhia te pūtakerua o te 100.
n=\frac{2±10}{2}
Ko te tauaro o -2 ko 2.
n=\frac{12}{2}
Nā, me whakaoti te whārite n=\frac{2±10}{2} ina he tāpiri te ±. Tāpiri 2 ki te 10.
n=6
Whakawehe 12 ki te 2.
n=-\frac{8}{2}
Nā, me whakaoti te whārite n=\frac{2±10}{2} ina he tango te ±. Tango 10 mai i 2.
n=-4
Whakawehe -8 ki te 2.
n^{2}-2n-24=\left(n-6\right)\left(n-\left(-4\right)\right)
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 6 mō te x_{1} me te -4 mō te x_{2}.
n^{2}-2n-24=\left(n-6\right)\left(n+4\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.