Whakaoti i te f(x)=7x^2+x-1

$$f ( x ) = 7 x ^ { 2 } + x - 1$$

Tauwehe

$$7\left(x-\frac{-\sqrt{29}-1}{14}\right)\left(x-\frac{\sqrt{29}-1}{14}\right)$$

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.

$$7x^{2}+x-1=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\times 7\left(-1\right)}}{2\times 7}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\times 7\left(-1\right)}}{2\times 7}$$

Whakareatia -4 ki te 7.

$$x=\frac{-1±\sqrt{1-28\left(-1\right)}}{2\times 7}$$

Whakareatia -28 ki te -1.

$$x=\frac{-1±\sqrt{1+28}}{2\times 7}$$

Tāpiri 1 ki te 28.

$$x=\frac{-1±\sqrt{29}}{2\times 7}$$

Whakareatia 2 ki te 7.

$$x=\frac{-1±\sqrt{29}}{14}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{29}}{14} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{29}.

$$x=\frac{\sqrt{29}-1}{14}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{29}}{14} ina he tango te ±. Tango \sqrt{29} mai i -1.

$$x=\frac{-\sqrt{29}-1}{14}$$

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{29}}{14} mō te x_{1} me te \frac{-1-\sqrt{29}}{14} mō te x_{2}.

$$7x^{2}+x-1=7\left(x-\frac{\sqrt{29}-1}{14}\right)\left(x-\frac{-\sqrt{29}-1}{14}\right)$$

Aromātai

$$7x^{2}+x-1$$