Whakaoti i te f(x)=3x^2+7x-8

$$f ( x ) = 3 x ^ { 2 } + 7 x - 8$$

Tauwehe

$$3\left(x-\frac{-\sqrt{145}-7}{6}\right)\left(x-\frac{\sqrt{145}-7}{6}\right)$$

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.

$$3x^{2}+7x-8=0$$

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.

$$x=\frac{-7±\sqrt{7^{2}-4\times 3\left(-8\right)}}{2\times 3}$$

Pūrua 7.

$$x=\frac{-7±\sqrt{49-4\times 3\left(-8\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-7±\sqrt{49-12\left(-8\right)}}{2\times 3}$$

Whakareatia -12 ki te -8.

$$x=\frac{-7±\sqrt{49+96}}{2\times 3}$$

Tāpiri 49 ki te 96.

$$x=\frac{-7±\sqrt{145}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{-7±\sqrt{145}}{6}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{145}}{6} ina he tāpiri te ±. Tāpiri -7 ki te \sqrt{145}.

$$x=\frac{\sqrt{145}-7}{6}$$

Nā, me whakaoti te whārite x=\frac{-7±\sqrt{145}}{6} ina he tango te ±. Tango \sqrt{145} mai i -7.

$$x=\frac{-\sqrt{145}-7}{6}$$

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{-7+\sqrt{145}}{6} mō te x_{1} me te \frac{-7-\sqrt{145}}{6} mō te x_{2}.

$$3x^{2}+7x-8=3\left(x-\frac{\sqrt{145}-7}{6}\right)\left(x-\frac{-\sqrt{145}-7}{6}\right)$$

Aromātai

$$3x^{2}+7x-8$$