Whakaoti i te f(x)=3x^2-15x+9

$$f ( x ) = 3 x ^ { 2 } - 15 x + 9$$

Tauwehe

$$3\left(x-\frac{5-\sqrt{13}}{2}\right)\left(x-\frac{\sqrt{13}+5}{2}\right)$$

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.

$$3x^{2}-15x+9=0$$

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.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 3\times 9}}{2\times 3}$$

Pūrua -15.

$$x=\frac{-\left(-15\right)±\sqrt{225-4\times 3\times 9}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-15\right)±\sqrt{225-12\times 9}}{2\times 3}$$

Whakareatia -12 ki te 9.

$$x=\frac{-\left(-15\right)±\sqrt{225-108}}{2\times 3}$$

Tāpiri 225 ki te -108.

$$x=\frac{-\left(-15\right)±\sqrt{117}}{2\times 3}$$

Tuhia te pūtakerua o te 117.

$$x=\frac{-\left(-15\right)±3\sqrt{13}}{2\times 3}$$

Ko te tauaro o -15 ko 15.

$$x=\frac{15±3\sqrt{13}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{15±3\sqrt{13}}{6}$$

Nā, me whakaoti te whārite x=\frac{15±3\sqrt{13}}{6} ina he tāpiri te ±. Tāpiri 15 ki te 3\sqrt{13}.

$$x=\frac{3\sqrt{13}+15}{6}$$

Whakawehe 15+3\sqrt{13} ki te 6.

$$x=\frac{\sqrt{13}+5}{2}$$

Nā, me whakaoti te whārite x=\frac{15±3\sqrt{13}}{6} ina he tango te ±. Tango 3\sqrt{13} mai i 15.

$$x=\frac{15-3\sqrt{13}}{6}$$

Whakawehe 15-3\sqrt{13} ki te 6.

$$x=\frac{5-\sqrt{13}}{2}$$

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{5+\sqrt{13}}{2} mō te x_{1} me te \frac{5-\sqrt{13}}{2} mō te x_{2}.

$$3x^{2}-15x+9=3\left(x-\frac{\sqrt{13}+5}{2}\right)\left(x-\frac{5-\sqrt{13}}{2}\right)$$

Aromātai

$$3\left(x^{2}-5x+3\right)$$