Whakaoti i te P(x)=3x^2-10x-6.quadD(x)=x-3

$$P ( x ) = 3 x ^ { 2 } - 10 x - 6 . \quad D ( x ) = x - 3$$

Tauwehe

$$3\left(x-\frac{5-\sqrt{43}}{3}\right)\left(x-\frac{\sqrt{43}+5}{3}\right)$$

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.

$$3x^{2}-10x-6=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 3\left(-6\right)}}{2\times 3}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\times 3\left(-6\right)}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-10\right)±\sqrt{100-12\left(-6\right)}}{2\times 3}$$

Whakareatia -12 ki te -6.

$$x=\frac{-\left(-10\right)±\sqrt{100+72}}{2\times 3}$$

Tāpiri 100 ki te 72.

$$x=\frac{-\left(-10\right)±\sqrt{172}}{2\times 3}$$

Tuhia te pūtakerua o te 172.

$$x=\frac{-\left(-10\right)±2\sqrt{43}}{2\times 3}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±2\sqrt{43}}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{10±2\sqrt{43}}{6}$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{43}}{6} ina he tāpiri te ±. Tāpiri 10 ki te 2\sqrt{43}.

$$x=\frac{2\sqrt{43}+10}{6}$$

Whakawehe 10+2\sqrt{43} ki te 6.

$$x=\frac{\sqrt{43}+5}{3}$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{43}}{6} ina he tango te ±. Tango 2\sqrt{43} mai i 10.

$$x=\frac{10-2\sqrt{43}}{6}$$

Whakawehe 10-2\sqrt{43} ki te 6.

$$x=\frac{5-\sqrt{43}}{3}$$

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+\sqrt{43}}{3} mō te x_{1} me te \frac{5-\sqrt{43}}{3} mō te x_{2}.

$$3x^{2}-10x-6=3\left(x-\frac{\sqrt{43}+5}{3}\right)\left(x-\frac{5-\sqrt{43}}{3}\right)$$

Aromātai

$$3x^{2}-10x-6$$