Whakaoti i te f(x)=4x^2-17x+3

$$f ( x ) = 4 x ^ { 2 } - 17 x + 3$$

Tauwehe

$$4\left(x-\frac{17-\sqrt{241}}{8}\right)\left(x-\frac{\sqrt{241}+17}{8}\right)$$

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.

$$4x^{2}-17x+3=0$$

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.

$$x=\frac{-\left(-17\right)±\sqrt{\left(-17\right)^{2}-4\times 4\times 3}}{2\times 4}$$

Pūrua -17.

$$x=\frac{-\left(-17\right)±\sqrt{289-4\times 4\times 3}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-\left(-17\right)±\sqrt{289-16\times 3}}{2\times 4}$$

Whakareatia -16 ki te 3.

$$x=\frac{-\left(-17\right)±\sqrt{289-48}}{2\times 4}$$

Tāpiri 289 ki te -48.

$$x=\frac{-\left(-17\right)±\sqrt{241}}{2\times 4}$$

Ko te tauaro o -17 ko 17.

$$x=\frac{17±\sqrt{241}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{17±\sqrt{241}}{8}$$

Nā, me whakaoti te whārite x=\frac{17±\sqrt{241}}{8} ina he tāpiri te ±. Tāpiri 17 ki te \sqrt{241}.

$$x=\frac{\sqrt{241}+17}{8}$$

Nā, me whakaoti te whārite x=\frac{17±\sqrt{241}}{8} ina he tango te ±. Tango \sqrt{241} mai i 17.

$$x=\frac{17-\sqrt{241}}{8}$$

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{17+\sqrt{241}}{8} mō te x_{1} me te \frac{17-\sqrt{241}}{8} mō te x_{2}.

$$4x^{2}-17x+3=4\left(x-\frac{\sqrt{241}+17}{8}\right)\left(x-\frac{17-\sqrt{241}}{8}\right)$$

Aromātai

$$4x^{2}-17x+3$$