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

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

Tauwehe

$$-\left(x-\left(3-\sqrt{14}\right)\right)\left(x-\left(\sqrt{14}+3\right)\right)$$

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.

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

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.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Pūrua 6.

$$x=\frac{-6±\sqrt{36-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

Whakareatia -4 ki te -1.

$$x=\frac{-6±\sqrt{36+4\times 5}}{2\left(-1\right)}$$

Whakareatia 4 ki te 5.

$$x=\frac{-6±\sqrt{36+20}}{2\left(-1\right)}$$

Tāpiri 36 ki te 20.

$$x=\frac{-6±\sqrt{56}}{2\left(-1\right)}$$

Tuhia te pūtakerua o te 56.

$$x=\frac{-6±2\sqrt{14}}{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$x=\frac{-6±2\sqrt{14}}{-2}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{14}}{-2} ina he tāpiri te ±. Tāpiri -6 ki te 2\sqrt{14}.

$$x=\frac{2\sqrt{14}-6}{-2}$$

Whakawehe -6+2\sqrt{14} ki te -2.

$$x=3-\sqrt{14}$$

Nā, me whakaoti te whārite x=\frac{-6±2\sqrt{14}}{-2} ina he tango te ±. Tango 2\sqrt{14} mai i -6.

$$x=\frac{-2\sqrt{14}-6}{-2}$$

Whakawehe -6-2\sqrt{14} ki te -2.

$$x=\sqrt{14}+3$$

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 3-\sqrt{14} mō te x_{1} me te 3+\sqrt{14} mō te x_{2}.

$$-x^{2}+6x+5=-\left(x-\left(3-\sqrt{14}\right)\right)\left(x-\left(\sqrt{14}+3\right)\right)$$

Aromātai

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