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a+b=-1 ab=1\left(-2\right)=-2
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=-2 b=1
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. Ko te takirua anake pērā ko te otinga pūnaha.
\left(x^{2}-2x\right)+\left(x-2\right)
Tuhia anō te x^{2}-x-2 hei \left(x^{2}-2x\right)+\left(x-2\right).
x\left(x-2\right)+x-2
Whakatauwehea atu x i te x^{2}-2x.
\left(x-2\right)\left(x+1\right)
Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}-x-2=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.
x=\frac{-\left(-1\right)±\sqrt{1-4\left(-2\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.
x=\frac{-\left(-1\right)±\sqrt{1+8}}{2}
Whakareatia -4 ki te -2.
x=\frac{-\left(-1\right)±\sqrt{9}}{2}
Tāpiri 1 ki te 8.
x=\frac{-\left(-1\right)±3}{2}
Tuhia te pūtakerua o te 9.
x=\frac{1±3}{2}
Ko te tauaro o -1 ko 1.
x=\frac{4}{2}
Nā, me whakaoti te whārite x=\frac{1±3}{2} ina he tāpiri te ±. Tāpiri 1 ki te 3.
x=2
Whakawehe 4 ki te 2.
x=-\frac{2}{2}
Nā, me whakaoti te whārite x=\frac{1±3}{2} ina he tango te ±. Tango 3 mai i 1.
x=-1
Whakawehe -2 ki te 2.
x^{2}-x-2=\left(x-2\right)\left(x-\left(-1\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 2 mō te x_{1} me te -1 mō te x_{2}.
x^{2}-x-2=\left(x-2\right)\left(x+1\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.