Whakaoti i te 10x^2-12x-4

$$10 { x }^{ 2 } -12x-4$$

Tauwehe

$$10\left(x-\frac{3-\sqrt{19}}{5}\right)\left(x-\frac{\sqrt{19}+3}{5}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

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.

$$10x^{2}-12x-4=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 10\left(-4\right)}}{2\times 10}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 10\left(-4\right)}}{2\times 10}$$

Whakareatia -4 ki te 10.

$$x=\frac{-\left(-12\right)±\sqrt{144-40\left(-4\right)}}{2\times 10}$$

Whakareatia -40 ki te -4.

$$x=\frac{-\left(-12\right)±\sqrt{144+160}}{2\times 10}$$

Tāpiri 144 ki te 160.

$$x=\frac{-\left(-12\right)±\sqrt{304}}{2\times 10}$$

Tuhia te pūtakerua o te 304.

$$x=\frac{-\left(-12\right)±4\sqrt{19}}{2\times 10}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±4\sqrt{19}}{2\times 10}$$

Whakareatia 2 ki te 10.

$$x=\frac{12±4\sqrt{19}}{20}$$

Nā, me whakaoti te whārite x=\frac{12±4\sqrt{19}}{20} ina he tāpiri te ±. Tāpiri 12 ki te 4\sqrt{19}.

$$x=\frac{4\sqrt{19}+12}{20}$$

Whakawehe 12+4\sqrt{19} ki te 20.

$$x=\frac{\sqrt{19}+3}{5}$$

Nā, me whakaoti te whārite x=\frac{12±4\sqrt{19}}{20} ina he tango te ±. Tango 4\sqrt{19} mai i 12.

$$x=\frac{12-4\sqrt{19}}{20}$$

Whakawehe 12-4\sqrt{19} ki te 20.

$$x=\frac{3-\sqrt{19}}{5}$$

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{3+\sqrt{19}}{5} mō te x_{1} me te \frac{3-\sqrt{19}}{5} mō te x_{2}.

$$10x^{2}-12x-4=10\left(x-\frac{\sqrt{19}+3}{5}\right)\left(x-\frac{3-\sqrt{19}}{5}\right)$$

Aromātai

$$10x^{2}-12x-4$$