Whakaoti i te 4x^2+5x-8

$$4 { x }^{ 2 } +5x-8$$

Tauwehe

$$4\left(x-\frac{-3\sqrt{17}-5}{8}\right)\left(x-\frac{3\sqrt{17}-5}{8}\right)$$

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.

$$4x^{2}+5x-8=0$$

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.

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

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\times 4\left(-8\right)}}{2\times 4}$$

Whakareatia -4 ki te 4.

$$x=\frac{-5±\sqrt{25-16\left(-8\right)}}{2\times 4}$$

Whakareatia -16 ki te -8.

$$x=\frac{-5±\sqrt{25+128}}{2\times 4}$$

Tāpiri 25 ki te 128.

$$x=\frac{-5±\sqrt{153}}{2\times 4}$$

Tuhia te pūtakerua o te 153.

$$x=\frac{-5±3\sqrt{17}}{2\times 4}$$

Whakareatia 2 ki te 4.

$$x=\frac{-5±3\sqrt{17}}{8}$$

Nā, me whakaoti te whārite x=\frac{-5±3\sqrt{17}}{8} ina he tāpiri te ±. Tāpiri -5 ki te 3\sqrt{17}.

$$x=\frac{3\sqrt{17}-5}{8}$$

Nā, me whakaoti te whārite x=\frac{-5±3\sqrt{17}}{8} ina he tango te ±. Tango 3\sqrt{17} mai i -5.

$$x=\frac{-3\sqrt{17}-5}{8}$$

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+3\sqrt{17}}{8} mō te x_{1} me te \frac{-5-3\sqrt{17}}{8} mō te x_{2}.

$$4x^{2}+5x-8=4\left(x-\frac{3\sqrt{17}-5}{8}\right)\left(x-\frac{-3\sqrt{17}-5}{8}\right)$$

Aromātai

$$4x^{2}+5x-8$$