Whakaoti i te 1-4x^2+x+9

$$1-4 { x }^{ 2 } +x+9$$

Tauwehe

$$-4\left(x-\frac{1-\sqrt{161}}{8}\right)\left(x-\frac{\sqrt{161}+1}{8}\right)$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Tāpirihia te 1 ki te 9, ka 10.

$$factor(10-4x^{2}+x)$$

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.

$$-4x^{2}+x+10=0$$

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-4\right)\times 10}}{2\left(-4\right)}$$

Pūrua 1.

$$x=\frac{-1±\sqrt{1-4\left(-4\right)\times 10}}{2\left(-4\right)}$$

Whakareatia -4 ki te -4.

$$x=\frac{-1±\sqrt{1+16\times 10}}{2\left(-4\right)}$$

Whakareatia 16 ki te 10.

$$x=\frac{-1±\sqrt{1+160}}{2\left(-4\right)}$$

Tāpiri 1 ki te 160.

$$x=\frac{-1±\sqrt{161}}{2\left(-4\right)}$$

Whakareatia 2 ki te -4.

$$x=\frac{-1±\sqrt{161}}{-8}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{161}}{-8} ina he tāpiri te ±. Tāpiri -1 ki te \sqrt{161}.

$$x=\frac{\sqrt{161}-1}{-8}$$

Whakawehe -1+\sqrt{161} ki te -8.

$$x=\frac{1-\sqrt{161}}{8}$$

Nā, me whakaoti te whārite x=\frac{-1±\sqrt{161}}{-8} ina he tango te ±. Tango \sqrt{161} mai i -1.

$$x=\frac{-\sqrt{161}-1}{-8}$$

Whakawehe -1-\sqrt{161} ki te -8.

$$x=\frac{\sqrt{161}+1}{8}$$

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{1-\sqrt{161}}{8} mō te x_{1} me te \frac{1+\sqrt{161}}{8} mō te x_{2}.

$$-4x^{2}+x+10=-4\left(x-\frac{1-\sqrt{161}}{8}\right)\left(x-\frac{\sqrt{161}+1}{8}\right)$$

Aromātai

$$10+x-4x^{2}$$

Ngā Upane Otinga

Tāpirihia te 1 ki te 9, ka 10.

$$10-4x^{2}+x$$