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

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

Tauwehe

$$3\left(x-\left(-\frac{\sqrt{33}}{6}-\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{33}}{6}-\frac{1}{2}\right)\right)$$

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.

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

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.

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

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\times 3\left(-2\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-3±\sqrt{9-12\left(-2\right)}}{2\times 3}$$

Whakareatia -12 ki te -2.

$$x=\frac{-3±\sqrt{9+24}}{2\times 3}$$

Tāpiri 9 ki te 24.

$$x=\frac{-3±\sqrt{33}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-3±\sqrt{33}}{6}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{33}}{6} ina he tāpiri te ±. Tāpiri -3 ki te \sqrt{33}.

$$x=\frac{\sqrt{33}-3}{6}$$

Whakawehe -3+\sqrt{33} ki te 6.

$$x=\frac{\sqrt{33}}{6}-\frac{1}{2}$$

Nā, me whakaoti te whārite x=\frac{-3±\sqrt{33}}{6} ina he tango te ±. Tango \sqrt{33} mai i -3.

$$x=\frac{-\sqrt{33}-3}{6}$$

Whakawehe -3-\sqrt{33} ki te 6.

$$x=-\frac{\sqrt{33}}{6}-\frac{1}{2}$$

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}{2}+\frac{\sqrt{33}}{6} mō te x_{1} me te -\frac{1}{2}-\frac{\sqrt{33}}{6} mō te x_{2}.

$$3x^{2}+3x-2=3\left(x-\left(\frac{\sqrt{33}}{6}-\frac{1}{2}\right)\right)\left(x-\left(-\frac{\sqrt{33}}{6}-\frac{1}{2}\right)\right)$$

Aromātai

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