Whakaoti i te 21t^2-12t+3

$$21 { t }^{ 2 } -12t+3$$

Tauwehe

$$3\left(7t^{2}-4t+1\right)$$

Ngā Upane Otinga

Tauwehea te 3. Kāore te pūrau 7t^{2}-4t+1 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$3\left(7t^{2}-4t+1\right)$$

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.

$$21t^{2}-12t+3=0$$

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.

$$t=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 21\times 3}}{2\times 21}$$

Pūrua -12.

$$t=\frac{-\left(-12\right)±\sqrt{144-4\times 21\times 3}}{2\times 21}$$

Whakareatia -4 ki te 21.

$$t=\frac{-\left(-12\right)±\sqrt{144-84\times 3}}{2\times 21}$$

Whakareatia -84 ki te 3.

$$t=\frac{-\left(-12\right)±\sqrt{144-252}}{2\times 21}$$

Tāpiri 144 ki te -252.

$$t=\frac{-\left(-12\right)±\sqrt{-108}}{2\times 21}$$

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.

$$21t^{2}-12t+3$$

Aromātai

$$21t^{2}-12t+3$$