Tauwehe
\left(x-2\right)\left(5x-1\right)
Aromātai
\left(x-2\right)\left(5x-1\right)
Graph
Tohaina
Kua tāruatia ki te papatopenga
a+b=-11 ab=5\times 2=10
Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 5x^{2}+ax+bx+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
-1,-10 -2,-5
I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 10.
-1-10=-11 -2-5=-7
Tātaihia te tapeke mō ia takirua.
a=-10 b=-1
Ko te otinga te takirua ka hoatu i te tapeke -11.
\left(5x^{2}-10x\right)+\left(-x+2\right)
Tuhia anō te 5x^{2}-11x+2 hei \left(5x^{2}-10x\right)+\left(-x+2\right).
5x\left(x-2\right)-\left(x-2\right)
Tauwehea te 5x i te tuatahi me te -1 i te rōpū tuarua.
\left(x-2\right)\left(5x-1\right)
Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.
5x^{2}-11x+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(-11\right)±\sqrt{\left(-11\right)^{2}-4\times 5\times 2}}{2\times 5}
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(-11\right)±\sqrt{121-4\times 5\times 2}}{2\times 5}
Pūrua -11.
x=\frac{-\left(-11\right)±\sqrt{121-20\times 2}}{2\times 5}
Whakareatia -4 ki te 5.
x=\frac{-\left(-11\right)±\sqrt{121-40}}{2\times 5}
Whakareatia -20 ki te 2.
x=\frac{-\left(-11\right)±\sqrt{81}}{2\times 5}
Tāpiri 121 ki te -40.
x=\frac{-\left(-11\right)±9}{2\times 5}
Tuhia te pūtakerua o te 81.
x=\frac{11±9}{2\times 5}
Ko te tauaro o -11 ko 11.
x=\frac{11±9}{10}
Whakareatia 2 ki te 5.
x=\frac{20}{10}
Nā, me whakaoti te whārite x=\frac{11±9}{10} ina he tāpiri te ±. Tāpiri 11 ki te 9.
x=2
Whakawehe 20 ki te 10.
x=\frac{2}{10}
Nā, me whakaoti te whārite x=\frac{11±9}{10} ina he tango te ±. Tango 9 mai i 11.
x=\frac{1}{5}
Whakahekea te hautanga \frac{2}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.
5x^{2}-11x+2=5\left(x-2\right)\left(x-\frac{1}{5}\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 \frac{1}{5} mō te x_{2}.
5x^{2}-11x+2=5\left(x-2\right)\times \frac{5x-1}{5}
Tango \frac{1}{5} 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.
5x^{2}-11x+2=\left(x-2\right)\left(5x-1\right)
Whakakorea atu te tauwehe pūnoa nui rawa 5 i roto i te 5 me te 5.
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