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

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

Tauwehe

$$2\left(x-\frac{-\sqrt{3}-1}{2}\right)\left(x-\frac{\sqrt{3}-1}{2}\right)$$

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.

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

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.

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

Pūrua 2.

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

Whakareatia -4 ki te 2.

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

Whakareatia -8 ki te -1.

$$x=\frac{-2±\sqrt{4+8}}{2\times 2}$$

Tāpiri 4 ki te 8.

$$x=\frac{-2±\sqrt{12}}{2\times 2}$$

Tuhia te pūtakerua o te 12.

$$x=\frac{-2±2\sqrt{3}}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-2±2\sqrt{3}}{4}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{3}}{4} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{3}.

$$x=\frac{2\sqrt{3}-2}{4}$$

Whakawehe -2+2\sqrt{3} ki te 4.

$$x=\frac{\sqrt{3}-1}{2}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{3}}{4} ina he tango te ±. Tango 2\sqrt{3} mai i -2.

$$x=\frac{-2\sqrt{3}-2}{4}$$

Whakawehe -2-2\sqrt{3} ki te 4.

$$x=\frac{-\sqrt{3}-1}{2}$$

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

$$2x^{2}+2x-1=2\left(x-\frac{\sqrt{3}-1}{2}\right)\left(x-\frac{-\sqrt{3}-1}{2}\right)$$

Aromātai

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