Whakaoti i te 3x^2+6x-1

$$3 x ^ { 2 } + 6 x - 1$$

Tauwehe

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

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.

$$3x^{2}+6x-1=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\times 3\left(-1\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-6±\sqrt{36-12\left(-1\right)}}{2\times 3}$$

Whakareatia -12 ki te -1.

$$x=\frac{-6±\sqrt{36+12}}{2\times 3}$$

Tāpiri 36 ki te 12.

$$x=\frac{-6±\sqrt{48}}{2\times 3}$$

Tuhia te pūtakerua o te 48.

$$x=\frac{-6±4\sqrt{3}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-6±4\sqrt{3}}{6}$$

Nā, me whakaoti te whārite x=\frac{-6±4\sqrt{3}}{6} ina he tāpiri te ±. Tāpiri -6 ki te 4\sqrt{3}.

$$x=\frac{4\sqrt{3}-6}{6}$$

Whakawehe -6+4\sqrt{3} ki te 6.

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

Nā, me whakaoti te whārite x=\frac{-6±4\sqrt{3}}{6} ina he tango te ±. Tango 4\sqrt{3} mai i -6.

$$x=\frac{-4\sqrt{3}-6}{6}$$

Whakawehe -6-4\sqrt{3} ki te 6.

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

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

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

Aromātai

$$3x^{2}+6x-1$$