Whakaoti i te f(x)=-2x^2+5x+6

$$f ( x ) = - 2 x ^ { 2 } + 5 x + 6$$

Tauwehe

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

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.

$$-2x^{2}+5x+6=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-2\right)\times 6}}{2\left(-2\right)}$$

Pūrua 5.

$$x=\frac{-5±\sqrt{25-4\left(-2\right)\times 6}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$x=\frac{-5±\sqrt{25+8\times 6}}{2\left(-2\right)}$$

Whakareatia 8 ki te 6.

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

Tāpiri 25 ki te 48.

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

Whakareatia 2 ki te -2.

$$x=\frac{-5±\sqrt{73}}{-4}$$

Nā, me whakaoti te whārite x=\frac{-5±\sqrt{73}}{-4} ina he tāpiri te ±. Tāpiri -5 ki te \sqrt{73}.

$$x=\frac{\sqrt{73}-5}{-4}$$

Whakawehe -5+\sqrt{73} ki te -4.

$$x=\frac{5-\sqrt{73}}{4}$$

Nā, me whakaoti te whārite x=\frac{-5±\sqrt{73}}{-4} ina he tango te ±. Tango \sqrt{73} mai i -5.

$$x=\frac{-\sqrt{73}-5}{-4}$$

Whakawehe -5-\sqrt{73} ki te -4.

$$x=\frac{\sqrt{73}+5}{4}$$

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}}{4} mō te x_{1} me te \frac{5+\sqrt{73}}{4} mō te x_{2}.

$$-2x^{2}+5x+6=-2\left(x-\frac{5-\sqrt{73}}{4}\right)\left(x-\frac{\sqrt{73}+5}{4}\right)$$

Aromātai

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