Whakaoti i te f(x)=x^2+6x-1

$$f ( x ) = x ^ { 2 } + 6 x - 1$$

Tauwehe

$$\left(x-\left(-\sqrt{10}-3\right)\right)\left(x-\left(\sqrt{10}-3\right)\right)$$

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.

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

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.

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

Pūrua 6.

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

Whakareatia -4 ki te -1.

$$x=\frac{-6±\sqrt{36+4}}{2}$$

Tāpiri 36 ki te 4.

$$x=\frac{-6±\sqrt{40}}{2}$$

Tuhia te pūtakerua o te 40.

$$x=\frac{-6±2\sqrt{10}}{2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{10}}{2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{10}.

$$x=\frac{2\sqrt{10}-6}{2}$$

Whakawehe -6+2\sqrt{10} ki te 2.

$$x=\sqrt{10}-3$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{10}}{2} ina he tango te ±. Tango 2\sqrt{10} mai i -6.

$$x=\frac{-2\sqrt{10}-6}{2}$$

Whakawehe -6-2\sqrt{10} ki te 2.

$$x=-\sqrt{10}-3$$

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 -3+\sqrt{10} mō te x_{1} me te -3-\sqrt{10} mō te x_{2}.

$$x^{2}+6x-1=\left(x-\left(\sqrt{10}-3\right)\right)\left(x-\left(-\sqrt{10}-3\right)\right)$$

Aromātai

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