Whakaoti i te f(x)=-125x^2+1375x-1500

$$f ( x ) = - 125 x ^ { 2 } + 1375 x - 1500$$

Tauwehe

$$-125\left(x-\frac{11-\sqrt{73}}{2}\right)\left(x-\frac{\sqrt{73}+11}{2}\right)$$

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.

$$-125x^{2}+1375x-1500=0$$

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.

$$x=\frac{-1375±\sqrt{1375^{2}-4\left(-125\right)\left(-1500\right)}}{2\left(-125\right)}$$

Pūrua 1375.

$$x=\frac{-1375±\sqrt{1890625-4\left(-125\right)\left(-1500\right)}}{2\left(-125\right)}$$

Whakareatia -4 ki te -125.

$$x=\frac{-1375±\sqrt{1890625+500\left(-1500\right)}}{2\left(-125\right)}$$

Whakareatia 500 ki te -1500.

$$x=\frac{-1375±\sqrt{1890625-750000}}{2\left(-125\right)}$$

Tāpiri 1890625 ki te -750000.

$$x=\frac{-1375±\sqrt{1140625}}{2\left(-125\right)}$$

Tuhia te pūtakerua o te 1140625.

$$x=\frac{-1375±125\sqrt{73}}{2\left(-125\right)}$$

Whakareatia 2 ki te -125.

$$x=\frac{-1375±125\sqrt{73}}{-250}$$

Nā, me whakaoti te whārite x=\frac{-1375±125\sqrt{73}}{-250} ina he tāpiri te ±. Tāpiri -1375 ki te 125\sqrt{73}.

$$x=\frac{125\sqrt{73}-1375}{-250}$$

Whakawehe -1375+125\sqrt{73} ki te -250.

$$x=\frac{11-\sqrt{73}}{2}$$

Nā, me whakaoti te whārite x=\frac{-1375±125\sqrt{73}}{-250} ina he tango te ±. Tango 125\sqrt{73} mai i -1375.

$$x=\frac{-125\sqrt{73}-1375}{-250}$$

Whakawehe -1375-125\sqrt{73} ki te -250.

$$x=\frac{\sqrt{73}+11}{2}$$

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{11-\sqrt{73}}{2} mō te x_{1} me te \frac{11+\sqrt{73}}{2} mō te x_{2}.

$$-125x^{2}+1375x-1500=-125\left(x-\frac{11-\sqrt{73}}{2}\right)\left(x-\frac{\sqrt{73}+11}{2}\right)$$

Aromātai

$$-125x^{2}+1375x-1500$$