Whakaoti i te f(x)=2x^2-4x-1

$$f ( x ) = 2 x ^ { 2 } - 4 x - 1$$

Tauwehe

$$2\left(x-\left(-\frac{\sqrt{6}}{2}+1\right)\right)\left(x-\left(\frac{\sqrt{6}}{2}+1\right)\right)$$

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.

$$2x^{2}-4x-1=0$$

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.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

Pūrua -4.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 2\left(-1\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-4\right)±\sqrt{16-8\left(-1\right)}}{2\times 2}$$

Whakareatia -8 ki te -1.

$$x=\frac{-\left(-4\right)±\sqrt{16+8}}{2\times 2}$$

Tāpiri 16 ki te 8.

$$x=\frac{-\left(-4\right)±\sqrt{24}}{2\times 2}$$

Tuhia te pūtakerua o te 24.

$$x=\frac{-\left(-4\right)±2\sqrt{6}}{2\times 2}$$

Ko te tauaro o -4 ko 4.

$$x=\frac{4±2\sqrt{6}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{4±2\sqrt{6}}{4}$$

Nā, me whakaoti te whārite x=\frac{4±2\sqrt{6}}{4} ina he tāpiri te ±. Tāpiri 4 ki te 2\sqrt{6}.

$$x=\frac{2\sqrt{6}+4}{4}$$

Whakawehe 4+2\sqrt{6} ki te 4.

$$x=\frac{\sqrt{6}}{2}+1$$

Nā, me whakaoti te whārite x=\frac{4±2\sqrt{6}}{4} ina he tango te ±. Tango 2\sqrt{6} mai i 4.

$$x=\frac{4-2\sqrt{6}}{4}$$

Whakawehe 4-2\sqrt{6} ki te 4.

$$x=-\frac{\sqrt{6}}{2}+1$$

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 1+\frac{\sqrt{6}}{2} mō te x_{1} me te 1-\frac{\sqrt{6}}{2} mō te x_{2}.

$$2x^{2}-4x-1=2\left(x-\left(\frac{\sqrt{6}}{2}+1\right)\right)\left(x-\left(-\frac{\sqrt{6}}{2}+1\right)\right)$$

Aromātai

$$2x^{2}-4x-1$$