Whakaoti i te f(x)=-2x^2+8x+4

$$f ( x ) = - 2 x ^ { 2 } + 8 x + 4$$

Tauwehe

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

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.

$$-2x^{2}+8x+4=0$$

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.

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

Pūrua 8.

$$x=\frac{-8±\sqrt{64-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-8±\sqrt{64+8\times 4}}{2\left(-2\right)}$$

Whakareatia 8 ki te 4.

$$x=\frac{-8±\sqrt{64+32}}{2\left(-2\right)}$$

Tāpiri 64 ki te 32.

$$x=\frac{-8±\sqrt{96}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 96.

$$x=\frac{-8±4\sqrt{6}}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$x=\frac{-8±4\sqrt{6}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{6}}{-4} ina he tāpiri te ±. Tāpiri -8 ki te 4\sqrt{6}.

$$x=\frac{4\sqrt{6}-8}{-4}$$

Whakawehe -8+4\sqrt{6} ki te -4.

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

Nā, me whakaoti te whārite x=\frac{-8±4\sqrt{6}}{-4} ina he tango te ±. Tango 4\sqrt{6} mai i -8.

$$x=\frac{-4\sqrt{6}-8}{-4}$$

Whakawehe -8-4\sqrt{6} ki te -4.

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

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

$$-2x^{2}+8x+4=-2\left(x-\left(2-\sqrt{6}\right)\right)\left(x-\left(\sqrt{6}+2\right)\right)$$

Aromātai

$$4+8x-2x^{2}$$