Whakaoti i te -0125x^3+15x^2-x-12

$$-0125 { x }^{ 3 } +15 { x }^{ 2 } -x-12$$

Aromātai

$$15x^{2}-x-12$$

Ngā Upane Otinga

Whakareatia te 0 ki te 125, ka 0.

$$0x^{3}+15x^{2}-x-12$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$0+15x^{2}-x-12$$

Tangohia te 12 i te 0, ka -12.

$$-12+15x^{2}-x$$

Tauwehe

$$15\left(x-\frac{1-\sqrt{721}}{30}\right)\left(x-\frac{\sqrt{721}+1}{30}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakareatia te 0 ki te 125, ka 0.

$$factor(0x^{3}+15x^{2}-x-12)$$

Ko te tau i whakarea ki te kore ka hua ko te kore.

$$factor(0+15x^{2}-x-12)$$

Tangohia te 12 i te 0, ka -12.

$$factor(-12+15x^{2}-x)$$

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.

$$15x^{2}-x-12=0$$

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 15\left(-12\right)}}{2\times 15}$$

Whakareatia -4 ki te 15.

$$x=\frac{-\left(-1\right)±\sqrt{1-60\left(-12\right)}}{2\times 15}$$

Whakareatia -60 ki te -12.

$$x=\frac{-\left(-1\right)±\sqrt{1+720}}{2\times 15}$$

Tāpiri 1 ki te 720.

$$x=\frac{-\left(-1\right)±\sqrt{721}}{2\times 15}$$

Ko te tauaro o -1 ko 1.

$$x=\frac{1±\sqrt{721}}{2\times 15}$$

Whakareatia 2 ki te 15.

$$x=\frac{1±\sqrt{721}}{30}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{721}}{30} ina he tāpiri te ±. Tāpiri 1 ki te \sqrt{721}.

$$x=\frac{\sqrt{721}+1}{30}$$

Nā, me whakaoti te whārite x=\frac{1±\sqrt{721}}{30} ina he tango te ±. Tango \sqrt{721} mai i 1.

$$x=\frac{1-\sqrt{721}}{30}$$

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{721}}{30} mō te x_{1} me te \frac{1-\sqrt{721}}{30} mō te x_{2}.

$$15x^{2}-x-12=15\left(x-\frac{\sqrt{721}+1}{30}\right)\left(x-\frac{1-\sqrt{721}}{30}\right)$$