Whakaoti i te f(x)=2x^2-12x+22

$$f ( x ) = 2 x ^ { 2 } - 12 x + 22$$

Tauwehe

$$2\left(x^{2}-6x+11\right)$$

Ngā Upane Otinga

Tauwehea te 2. Kāore te pūrau x^{2}-6x+11 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$2\left(x^{2}-6x+11\right)$$

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.

$$2x^{2}-12x+22=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 2\times 22}}{2\times 2}$$

Pūrua -12.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 2\times 22}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-12\right)±\sqrt{144-8\times 22}}{2\times 2}$$

Whakareatia -8 ki te 22.

$$x=\frac{-\left(-12\right)±\sqrt{144-176}}{2\times 2}$$

Tāpiri 144 ki te -176.

$$x=\frac{-\left(-12\right)±\sqrt{-32}}{2\times 2}$$

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.

$$2x^{2}-12x+22$$

Aromātai

$$2\left(x^{2}-6x+11\right)$$