Whakaoti i te p(x)=-5x^2-10x-2

$$p ( x ) = - 5 x ^ { 2 } - 10 x - 2$$

Tauwehe

$$-5\left(x-\left(-\frac{\sqrt{15}}{5}-1\right)\right)\left(x-\left(\frac{\sqrt{15}}{5}-1\right)\right)$$

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.

$$-5x^{2}-10x-2=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-5\right)\left(-2\right)}}{2\left(-5\right)}$$

Pūrua -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\left(-5\right)\left(-2\right)}}{2\left(-5\right)}$$

Whakareatia -4 ki te -5.

$$x=\frac{-\left(-10\right)±\sqrt{100+20\left(-2\right)}}{2\left(-5\right)}$$

Whakareatia 20 ki te -2.

$$x=\frac{-\left(-10\right)±\sqrt{100-40}}{2\left(-5\right)}$$

Tāpiri 100 ki te -40.

$$x=\frac{-\left(-10\right)±\sqrt{60}}{2\left(-5\right)}$$

Tuhia te pūtakerua o te 60.

$$x=\frac{-\left(-10\right)±2\sqrt{15}}{2\left(-5\right)}$$

Ko te tauaro o -10 ko 10.

$$x=\frac{10±2\sqrt{15}}{2\left(-5\right)}$$

Whakareatia 2 ki te -5.

$$x=\frac{10±2\sqrt{15}}{-10}$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{15}}{-10} ina he tāpiri te ±. Tāpiri 10 ki te 2\sqrt{15}.

$$x=\frac{2\sqrt{15}+10}{-10}$$

Whakawehe 10+2\sqrt{15} ki te -10.

$$x=-\frac{\sqrt{15}}{5}-1$$

Nā, me whakaoti te whārite x=\frac{10±2\sqrt{15}}{-10} ina he tango te ±. Tango 2\sqrt{15} mai i 10.

$$x=\frac{10-2\sqrt{15}}{-10}$$

Whakawehe 10-2\sqrt{15} ki te -10.

$$x=\frac{\sqrt{15}}{5}-1$$

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 -1-\frac{\sqrt{15}}{5} mō te x_{1} me te -1+\frac{\sqrt{15}}{5} mō te x_{2}.

$$-5x^{2}-10x-2=-5\left(x-\left(-\frac{\sqrt{15}}{5}-1\right)\right)\left(x-\left(\frac{\sqrt{15}}{5}-1\right)\right)$$

Aromātai

$$-5x^{2}-10x-2$$