Whakaoti i te f(x)=2x^2-12/2x^2-5x+3

$$f ( x ) = 2 x ^ { 2 } - \frac { 12 } { 2 } x ^ { 2 } - 5 x + 3$$

Aromātai

$$3-5x-4x^{2}$$

Ngā Upane Otinga

Whakawehea te 12 ki te 2, kia riro ko 6.

$$2x^{2}-6x^{2}-5x+3$$

Pahekotia te 2x^{2} me -6x^{2}, ka -4x^{2}.

$$-4x^{2}-5x+3$$

Tauwehe

$$-4\left(x-\frac{-\sqrt{73}-5}{8}\right)\left(x-\frac{\sqrt{73}-5}{8}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakawehea te 12 ki te 2, kia riro ko 6.

$$factor(2x^{2}-6x^{2}-5x+3)$$

Pahekotia te 2x^{2} me -6x^{2}, ka -4x^{2}.

$$factor(-4x^{2}-5x+3)$$

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.

$$-4x^{2}-5x+3=0$$

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.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\left(-4\right)\times 3}}{2\left(-4\right)}$$

Pūrua -5.

$$x=\frac{-\left(-5\right)±\sqrt{25-4\left(-4\right)\times 3}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{-\left(-5\right)±\sqrt{25+16\times 3}}{2\left(-4\right)}$$

Whakareatia 16 ki te 3.

$$x=\frac{-\left(-5\right)±\sqrt{25+48}}{2\left(-4\right)}$$

Tāpiri 25 ki te 48.

$$x=\frac{-\left(-5\right)±\sqrt{73}}{2\left(-4\right)}$$

Ko te tauaro o -5 ko 5.

$$x=\frac{5±\sqrt{73}}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{5±\sqrt{73}}{-8}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{73}}{-8} ina he tāpiri te ±. Tāpiri 5 ki te \sqrt{73}.

$$x=\frac{\sqrt{73}+5}{-8}$$

Whakawehe 5+\sqrt{73} ki te -8.

$$x=\frac{-\sqrt{73}-5}{8}$$

Nā, me whakaoti te whārite x=\frac{5±\sqrt{73}}{-8} ina he tango te ±. Tango \sqrt{73} mai i 5.

$$x=\frac{5-\sqrt{73}}{-8}$$

Whakawehe 5-\sqrt{73} ki te -8.

$$x=\frac{\sqrt{73}-5}{8}$$

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{73}}{8} mō te x_{1} me te \frac{-5+\sqrt{73}}{8} mō te x_{2}.

$$-4x^{2}-5x+3=-4\left(x-\frac{-\sqrt{73}-5}{8}\right)\left(x-\frac{\sqrt{73}-5}{8}\right)$$