Whakaoti i te f(x)=3x-3x^2-12

$$f ( x ) = 3 x - 3 x ^ { 2 } - 12$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 3. Kāore te pūrau x-x^{2}-4 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$3\left(x-x^{2}-4\right)$$

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.

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

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.

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

Pūrua 3.

$$x=\frac{-3±\sqrt{9-4\left(-3\right)\left(-12\right)}}{2\left(-3\right)}$$

Whakareatia -4 ki te -3.

$$x=\frac{-3±\sqrt{9+12\left(-12\right)}}{2\left(-3\right)}$$

Whakareatia 12 ki te -12.

$$x=\frac{-3±\sqrt{9-144}}{2\left(-3\right)}$$

Tāpiri 9 ki te -144.

$$x=\frac{-3±\sqrt{-135}}{2\left(-3\right)}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā. Kāore e taea te pūrau pūrua te whakatauwehe.

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

Aromātai

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