Whakaoti i te f(x)=x^2+12x+6

$$f ( x ) = x ^ { 2 } + 12 x + 6$$

Tauwehe

$$\left(x-\left(-\sqrt{30}-6\right)\right)\left(x-\left(\sqrt{30}-6\right)\right)$$

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.

$$x^{2}+12x+6=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 6}}{2}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\times 6}}{2}$$

Whakareatia -4 ki te 6.

$$x=\frac{-12±\sqrt{144-24}}{2}$$

Tāpiri 144 ki te -24.

$$x=\frac{-12±\sqrt{120}}{2}$$

Tuhia te pūtakerua o te 120.

$$x=\frac{-12±2\sqrt{30}}{2}$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{30}}{2} ina he tāpiri te ±. Tāpiri -12 ki te 2\sqrt{30}.

$$x=\frac{2\sqrt{30}-12}{2}$$

Whakawehe -12+2\sqrt{30} ki te 2.

$$x=\sqrt{30}-6$$

Nā, me whakaoti te whārite x=\frac{-12±2\sqrt{30}}{2} ina he tango te ±. Tango 2\sqrt{30} mai i -12.

$$x=\frac{-2\sqrt{30}-12}{2}$$

Whakawehe -12-2\sqrt{30} ki te 2.

$$x=-\sqrt{30}-6$$

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 -6+\sqrt{30} mō te x_{1} me te -6-\sqrt{30} mō te x_{2}.

$$x^{2}+12x+6=\left(x-\left(\sqrt{30}-6\right)\right)\left(x-\left(-\sqrt{30}-6\right)\right)$$

Aromātai

$$x^{2}+12x+6$$