Whakaoti i te 3x^2-12x-11

$$3 x ^ { 2 } - 12 x - 11$$

Tauwehe

$$3\left(x-\left(-\frac{\sqrt{69}}{3}+2\right)\right)\left(x-\left(\frac{\sqrt{69}}{3}+2\right)\right)$$

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.

$$3x^{2}-12x-11=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 3\left(-11\right)}}{2\times 3}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 3\left(-11\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-12\right)±\sqrt{144-12\left(-11\right)}}{2\times 3}$$

Whakareatia -12 ki te -11.

$$x=\frac{-\left(-12\right)±\sqrt{144+132}}{2\times 3}$$

Tāpiri 144 ki te 132.

$$x=\frac{-\left(-12\right)±\sqrt{276}}{2\times 3}$$

Tuhia te pūtakerua o te 276.

$$x=\frac{-\left(-12\right)±2\sqrt{69}}{2\times 3}$$

Ko te tauaro o -12 ko 12.

$$x=\frac{12±2\sqrt{69}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{12±2\sqrt{69}}{6}$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{69}}{6} ina he tāpiri te ±. Tāpiri 12 ki te 2\sqrt{69}.

$$x=\frac{2\sqrt{69}+12}{6}$$

Whakawehe 12+2\sqrt{69} ki te 6.

$$x=\frac{\sqrt{69}}{3}+2$$

Nā, me whakaoti te whārite x=\frac{12±2\sqrt{69}}{6} ina he tango te ±. Tango 2\sqrt{69} mai i 12.

$$x=\frac{12-2\sqrt{69}}{6}$$

Whakawehe 12-2\sqrt{69} ki te 6.

$$x=-\frac{\sqrt{69}}{3}+2$$

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 2+\frac{\sqrt{69}}{3} mō te x_{1} me te 2-\frac{\sqrt{69}}{3} mō te x_{2}.

$$3x^{2}-12x-11=3\left(x-\left(\frac{\sqrt{69}}{3}+2\right)\right)\left(x-\left(-\frac{\sqrt{69}}{3}+2\right)\right)$$

Aromātai

$$3x^{2}-12x-11$$