Whakaoti i te 4x^2-5x-2

$$4 x ^ { 2 } - 5 x - 2$$

Tauwehe

$$4\left(x-\frac{5-\sqrt{57}}{8}\right)\left(x-\frac{\sqrt{57}+5}{8}\right)$$

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.

$$4x^{2}-5x-2=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 4\left(-2\right)}}{2\times 4}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\times 4\left(-2\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-\left(-5\right)±\sqrt{25-16\left(-2\right)}}{2\times 4}$$

Whakareatia -16 ki te -2.

$$x=\frac{-\left(-5\right)±\sqrt{25+32}}{2\times 4}$$

Tāpiri 25 ki te 32.

$$x=\frac{-\left(-5\right)±\sqrt{57}}{2\times 4}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±\sqrt{57}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{5±\sqrt{57}}{8}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{57}}{8} ina he tāpiri te ±. Tāpiri 5 ki te \sqrt{57}.

$$x=\frac{\sqrt{57}+5}{8}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{57}}{8} ina he tango te ±. Tango \sqrt{57} mai i 5.

$$x=\frac{5-\sqrt{57}}{8}$$

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{5+\sqrt{57}}{8} mō te x_{1} me te \frac{5-\sqrt{57}}{8} mō te x_{2}.

$$4x^{2}-5x-2=4\left(x-\frac{\sqrt{57}+5}{8}\right)\left(x-\frac{5-\sqrt{57}}{8}\right)$$

Aromātai

$$4x^{2}-5x-2$$