Whakaoti i te x^2+11x+3

$$x ^ { 2 } + 11 x + 3$$

Tauwehe

$$\left(x-\frac{-\sqrt{109}-11}{2}\right)\left(x-\frac{\sqrt{109}-11}{2}\right)$$

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.

$$x^{2}+11x+3=0$$

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.

$$x=\frac{-11±\sqrt{11^{2}-4\times 3}}{2}$$

Pūrua 11.

$$x=\frac{-11±\sqrt{121-4\times 3}}{2}$$

Whakareatia -4 ki te 3.

$$x=\frac{-11±\sqrt{121-12}}{2}$$

Tāpiri 121 ki te -12.

$$x=\frac{-11±\sqrt{109}}{2}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{109}}{2} ina he tāpiri te ±. Tāpiri -11 ki te \sqrt{109}.

$$x=\frac{\sqrt{109}-11}{2}$$

Nā, me whakaoti te whārite x=\frac{-11±\sqrt{109}}{2} ina he tango te ±. Tango \sqrt{109} mai i -11.

$$x=\frac{-\sqrt{109}-11}{2}$$

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{-11+\sqrt{109}}{2} mō te x_{1} me te \frac{-11-\sqrt{109}}{2} mō te x_{2}.

$$x^{2}+11x+3=\left(x-\frac{\sqrt{109}-11}{2}\right)\left(x-\frac{-\sqrt{109}-11}{2}\right)$$

Aromātai

$$x^{2}+11x+3$$