Whakaoti i te f(x)=3x^2+6x-2

$$f ( x ) = 3 x ^ { 2 } + 6 x - 2$$

Tauwehe

$$3\left(x-\left(-\frac{\sqrt{15}}{3}-1\right)\right)\left(x-\left(\frac{\sqrt{15}}{3}-1\right)\right)$$

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.

$$3x^{2}+6x-2=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 3\left(-2\right)}}{2\times 3}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\times 3\left(-2\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-6±\sqrt{36-12\left(-2\right)}}{2\times 3}$$

Whakareatia -12 ki te -2.

$$x=\frac{-6±\sqrt{36+24}}{2\times 3}$$

Tāpiri 36 ki te 24.

$$x=\frac{-6±\sqrt{60}}{2\times 3}$$

Tuhia te pūtakerua o te 60.

$$x=\frac{-6±2\sqrt{15}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-6±2\sqrt{15}}{6}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{15}}{6} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{15}.

$$x=\frac{2\sqrt{15}-6}{6}$$

Whakawehe -6+2\sqrt{15} ki te 6.

$$x=\frac{\sqrt{15}}{3}-1$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{15}}{6} ina he tango te ±. Tango 2\sqrt{15} mai i -6.

$$x=\frac{-2\sqrt{15}-6}{6}$$

Whakawehe -6-2\sqrt{15} ki te 6.

$$x=-\frac{\sqrt{15}}{3}-1$$

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{15}}{3} mō te x_{1} me te -1-\frac{\sqrt{15}}{3} mō te x_{2}.

$$3x^{2}+6x-2=3\left(x-\left(\frac{\sqrt{15}}{3}-1\right)\right)\left(x-\left(-\frac{\sqrt{15}}{3}-1\right)\right)$$

Aromātai

$$3x^{2}+6x-2$$