Whakaoti i te 3+12x-4x^2

$$3 + 12 x - 4 x ^ { 2 }$$

Tauwehe

$$-4\left(x-\left(\frac{3}{2}-\sqrt{3}\right)\right)\left(x-\left(\sqrt{3}+\frac{3}{2}\right)\right)$$

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.

$$-4x^{2}+12x+3=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\left(-4\right)\times 3}}{2\left(-4\right)}$$

Pūrua 12.

$$x=\frac{-12±\sqrt{144-4\left(-4\right)\times 3}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{-12±\sqrt{144+16\times 3}}{2\left(-4\right)}$$

Whakareatia 16 ki te 3.

$$x=\frac{-12±\sqrt{144+48}}{2\left(-4\right)}$$

Tāpiri 144 ki te 48.

$$x=\frac{-12±\sqrt{192}}{2\left(-4\right)}$$

Tuhia te pūtakerua o te 192.

$$x=\frac{-12±8\sqrt{3}}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-12±8\sqrt{3}}{-8}$$

Nā, me whakaoti te whārite x=\frac{-12±8\sqrt{3}}{-8} ina he tāpiri te ±. Tāpiri -12 ki te 8\sqrt{3}.

$$x=\frac{8\sqrt{3}-12}{-8}$$

Whakawehe -12+8\sqrt{3} ki te -8.

$$x=\frac{3}{2}-\sqrt{3}$$

Nā, me whakaoti te whārite x=\frac{-12±8\sqrt{3}}{-8} ina he tango te ±. Tango 8\sqrt{3} mai i -12.

$$x=\frac{-8\sqrt{3}-12}{-8}$$

Whakawehe -12-8\sqrt{3} ki te -8.

$$x=\sqrt{3}+\frac{3}{2}$$

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

$$-4x^{2}+12x+3=-4\left(x-\left(\frac{3}{2}-\sqrt{3}\right)\right)\left(x-\left(\sqrt{3}+\frac{3}{2}\right)\right)$$

Aromātai

$$3+12x-4x^{2}$$