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a+b=-5 ab=12\left(-2\right)=-24
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 12x^{2}+ax+bx-2. 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=-8 b=3
Ko te otinga te takirua ka hoatu i te tapeke -5.
\left(12x^{2}-8x\right)+\left(3x-2\right)
Tuhia anō te 12x^{2}-5x-2 hei \left(12x^{2}-8x\right)+\left(3x-2\right).
4x\left(3x-2\right)+3x-2
Whakatauwehea atu 4x i te 12x^{2}-8x.
\left(3x-2\right)\left(4x+1\right)
Whakatauwehea atu te kīanga pātahi 3x-2 mā te whakamahi i te āhuatanga tātai tohatoha.
12x^{2}-5x-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(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 12\left(-2\right)}}{2\times 12}
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(-5\right)±\sqrt{25-4\times 12\left(-2\right)}}{2\times 12}
Pūrua -5.
x=\frac{-\left(-5\right)±\sqrt{25-48\left(-2\right)}}{2\times 12}
Whakareatia -4 ki te 12.
x=\frac{-\left(-5\right)±\sqrt{25+96}}{2\times 12}
Whakareatia -48 ki te -2.
x=\frac{-\left(-5\right)±\sqrt{121}}{2\times 12}
Tāpiri 25 ki te 96.
x=\frac{-\left(-5\right)±11}{2\times 12}
Tuhia te pūtakerua o te 121.
x=\frac{5±11}{2\times 12}
Ko te tauaro o -5 ko 5.
x=\frac{5±11}{24}
Whakareatia 2 ki te 12.
x=\frac{16}{24}
Nā, me whakaoti te whārite x=\frac{5±11}{24} ina he tāpiri te ±. Tāpiri 5 ki te 11.
x=\frac{2}{3}
Whakahekea te hautanga \frac{16}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.
x=-\frac{6}{24}
Nā, me whakaoti te whārite x=\frac{5±11}{24} ina he tango te ±. Tango 11 mai i 5.
x=-\frac{1}{4}
Whakahekea te hautanga \frac{-6}{24} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.
12x^{2}-5x-2=12\left(x-\frac{2}{3}\right)\left(x-\left(-\frac{1}{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 \frac{2}{3} mō te x_{1} me te -\frac{1}{4} mō te x_{2}.
12x^{2}-5x-2=12\left(x-\frac{2}{3}\right)\left(x+\frac{1}{4}\right)
Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.
12x^{2}-5x-2=12\times \frac{3x-2}{3}\left(x+\frac{1}{4}\right)
Tango \frac{2}{3} mai i x mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
12x^{2}-5x-2=12\times \frac{3x-2}{3}\times \frac{4x+1}{4}
Tāpiri \frac{1}{4} ki te x mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
12x^{2}-5x-2=12\times \frac{\left(3x-2\right)\left(4x+1\right)}{3\times 4}
Whakareatia \frac{3x-2}{3} ki te \frac{4x+1}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.
12x^{2}-5x-2=12\times \frac{\left(3x-2\right)\left(4x+1\right)}{12}
Whakareatia 3 ki te 4.
12x^{2}-5x-2=\left(3x-2\right)\left(4x+1\right)
Whakakorea atu te tauwehe pūnoa nui rawa 12 i roto i te 12 me te 12.