Whakaoti i te 2x^3+6x^2+7x+60=0

$$2 { x }^{ 3 } +6 { x }^{ 2 } +7x+60 = 0$$

Whakaoti mō x (complex solution)

$$x=\frac{-\sqrt{29}i+1}{2}\approx 0.5-2.692582404i$$

$$x=-4$$

$$x=\frac{1+\sqrt{29}i}{2}\approx 0.5+2.692582404i$$

Ngā Upane Otinga

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau 60, ā, ka wehea e q te whakarea arahanga 2. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±30,±60,±15,±10,±20,±\frac{15}{2},±6,±12,±5,±3,±\frac{5}{2},±2,±4,±\frac{3}{2},±1,±\frac{1}{2}$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$x=-4$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te 2x^{3}+6x^{2}+7x+60 ki te x+4, kia riro ko 2x^{2}-2x+15. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$2x^{2}-2x+15=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 2 mō te a, te -2 mō te b, me te 15 mō te c i te ture pūrua.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2\times 15}}{2\times 2}$$

Mahia ngā tātaitai.

$$x=\frac{2±\sqrt{-116}}{4}$$

Whakaotia te whārite 2x^{2}-2x+15=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=\frac{-\sqrt{29}i+1}{2} x=\frac{1+\sqrt{29}i}{2}$$

Rārangitia ngā otinga katoa i kitea.

$$x=-4 x=\frac{-\sqrt{29}i+1}{2} x=\frac{1+\sqrt{29}i}{2}$$

Whakaoti mō x

$$x=-4$$

Ngā Upane Otinga

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau 60, ā, ka wehea e q te whakarea arahanga 2. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±30,±60,±15,±10,±20,±\frac{15}{2},±6,±12,±5,±3,±\frac{5}{2},±2,±4,±\frac{3}{2},±1,±\frac{1}{2}$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$x=-4$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te 2x^{3}+6x^{2}+7x+60 ki te x+4, kia riro ko 2x^{2}-2x+15. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$2x^{2}-2x+15=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 2 mō te a, te -2 mō te b, me te 15 mō te c i te ture pūrua.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2\times 15}}{2\times 2}$$

Mahia ngā tātaitai.

$$x=\frac{2±\sqrt{-116}}{4}$$

Tā te mea e kore te pūrua o tētahi tau tōraro e tautohutia ki te āpure tūturu, kāhore he rongoā.

$$x\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$x=-4$$