Whakaoti i te 3x^2+2x-4=

$$3 x ^ { 2 } + 2 x - 4 =$$

Tauwehe

$$3\left(x-\frac{-\sqrt{13}-1}{3}\right)\left(x-\frac{\sqrt{13}-1}{3}\right)$$

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.

$$3x^{2}+2x-4=0$$

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.

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

Pūrua 2.

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

Whakareatia -4 ki te 3.

$$x=\frac{-2±\sqrt{4-12\left(-4\right)}}{2\times 3}$$

Whakareatia -12 ki te -4.

$$x=\frac{-2±\sqrt{4+48}}{2\times 3}$$

Tāpiri 4 ki te 48.

$$x=\frac{-2±\sqrt{52}}{2\times 3}$$

Tuhia te pūtakerua o te 52.

$$x=\frac{-2±2\sqrt{13}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-2±2\sqrt{13}}{6}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{13}}{6} ina he tāpiri te ±. Tāpiri -2 ki te 2\sqrt{13}.

$$x=\frac{2\sqrt{13}-2}{6}$$

Whakawehe -2+2\sqrt{13} ki te 6.

$$x=\frac{\sqrt{13}-1}{3}$$

Nā, me whakaoti te whārite x=\frac{-2±2\sqrt{13}}{6} ina he tango te ±. Tango 2\sqrt{13} mai i -2.

$$x=\frac{-2\sqrt{13}-2}{6}$$

Whakawehe -2-2\sqrt{13} ki te 6.

$$x=\frac{-\sqrt{13}-1}{3}$$

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{13}}{3} mō te x_{1} me te \frac{-1-\sqrt{13}}{3} mō te x_{2}.

$$3x^{2}+2x-4=3\left(x-\frac{\sqrt{13}-1}{3}\right)\left(x-\frac{-\sqrt{13}-1}{3}\right)$$

Aromātai

$$3x^{2}+2x-4$$