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a+b=11 ab=1\times 24=24
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
1,24 2,12 3,8 4,6
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 24.
1+24=25 2+12=14 3+8=11 4+6=10
Tātaihia te tapeke mō ia takirua.
a=3 b=8
Ko te otinga te takirua ka hoatu i te tapeke 11.
\left(x^{2}+3x\right)+\left(8x+24\right)
Tuhia anō te x^{2}+11x+24 hei \left(x^{2}+3x\right)+\left(8x+24\right).
x\left(x+3\right)+8\left(x+3\right)
Tauwehea te x i te tuatahi me te 8 i te rōpū tuarua.
\left(x+3\right)\left(x+8\right)
Whakatauwehea atu te kīanga pātahi x+3 mā te whakamahi i te āhuatanga tātai tohatoha.
x^{2}+11x+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.
x=\frac{-11±\sqrt{11^{2}-4\times 24}}{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{-11±\sqrt{121-4\times 24}}{2}
Pūrua 11.
x=\frac{-11±\sqrt{121-96}}{2}
Whakareatia -4 ki te 24.
x=\frac{-11±\sqrt{25}}{2}
Tāpiri 121 ki te -96.
x=\frac{-11±5}{2}
Tuhia te pūtakerua o te 25.
x=-\frac{6}{2}
Nā, me whakaoti te whārite x=\frac{-11±5}{2} ina he tāpiri te ±. Tāpiri -11 ki te 5.
x=-3
Whakawehe -6 ki te 2.
x=-\frac{16}{2}
Nā, me whakaoti te whārite x=\frac{-11±5}{2} ina he tango te ±. Tango 5 mai i -11.
x=-8
Whakawehe -16 ki te 2.
x^{2}+11x+24=\left(x-\left(-3\right)\right)\left(x-\left(-8\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 -3 mō te x_{1} me te -8 mō te x_{2}.
x^{2}+11x+24=\left(x+3\right)\left(x+8\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.