Whakaoti i te 3b^2+15b+2

$$3 b ^ { 2 } + 15 b + 2$$

Tauwehe

$$3\left(b-\left(-\frac{\sqrt{201}}{6}-\frac{5}{2}\right)\right)\left(b-\left(\frac{\sqrt{201}}{6}-\frac{5}{2}\right)\right)$$

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.

$$3b^{2}+15b+2=0$$

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.

$$b=\frac{-15±\sqrt{15^{2}-4\times 3\times 2}}{2\times 3}$$

Pūrua 15.

$$b=\frac{-15±\sqrt{225-4\times 3\times 2}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$b=\frac{-15±\sqrt{225-12\times 2}}{2\times 3}$$

Whakareatia -12 ki te 2.

$$b=\frac{-15±\sqrt{225-24}}{2\times 3}$$

Tāpiri 225 ki te -24.

$$b=\frac{-15±\sqrt{201}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$b=\frac{-15±\sqrt{201}}{6}$$

Nā, me whakaoti te whārite b=\frac{-15±\sqrt{201}}{6} ina he tāpiri te ±. Tāpiri -15 ki te \sqrt{201}.

$$b=\frac{\sqrt{201}-15}{6}$$

Whakawehe -15+\sqrt{201} ki te 6.

$$b=\frac{\sqrt{201}}{6}-\frac{5}{2}$$

Nā, me whakaoti te whārite b=\frac{-15±\sqrt{201}}{6} ina he tango te ±. Tango \sqrt{201} mai i -15.

$$b=\frac{-\sqrt{201}-15}{6}$$

Whakawehe -15-\sqrt{201} ki te 6.

$$b=-\frac{\sqrt{201}}{6}-\frac{5}{2}$$

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{5}{2}+\frac{\sqrt{201}}{6} mō te x_{1} me te -\frac{5}{2}-\frac{\sqrt{201}}{6} mō te x_{2}.

$$3b^{2}+15b+2=3\left(b-\left(\frac{\sqrt{201}}{6}-\frac{5}{2}\right)\right)\left(b-\left(-\frac{\sqrt{201}}{6}-\frac{5}{2}\right)\right)$$

Aromātai

$$3b^{2}+15b+2$$