Whakaoti i te 2z^3+3z^2+8z-5=0

$$2 z ^ { 3 } + 3 z ^ { 2 } + 8 z - 5 = 0$$

Whakaoti mō z (complex solution)

$$z=-1-2i$$

$$z=\frac{1}{2}=0.5$$

$$z=-1+2i$$

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 -5, ā, ka wehea e q te whakarea arahanga 2. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{5}{2},±5,±\frac{1}{2},±1$$

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.

$$z=\frac{1}{2}$$

Mā te whakatakotoranga Tauwehe, he tauwehe te z-k o te pūrau mō ia pūtake k. Whakawehea te 2z^{3}+3z^{2}+8z-5 ki te 2\left(z-\frac{1}{2}\right)=2z-1, kia riro ko z^{2}+2z+5. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$z^{2}+2z+5=0$$

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 1 mō te a, te 2 mō te b, me te 5 mō te c i te ture pūrua.

$$z=\frac{-2±\sqrt{2^{2}-4\times 1\times 5}}{2}$$

Mahia ngā tātaitai.

$$z=\frac{-2±\sqrt{-16}}{2}$$

Whakaotia te whārite z^{2}+2z+5=0 ina he tōrunga te ±, ina he tōraro te ±.

$$z=-1-2i z=-1+2i$$

Rārangitia ngā otinga katoa i kitea.

$$z=\frac{1}{2} z=-1-2i z=-1+2i$$

Whakaoti mō z

$$z=\frac{1}{2}=0.5$$

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 -5, ā, ka wehea e q te whakarea arahanga 2. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±\frac{5}{2},±5,±\frac{1}{2},±1$$

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.

$$z=\frac{1}{2}$$

Mā te whakatakotoranga Tauwehe, he tauwehe te z-k o te pūrau mō ia pūtake k. Whakawehea te 2z^{3}+3z^{2}+8z-5 ki te 2\left(z-\frac{1}{2}\right)=2z-1, kia riro ko z^{2}+2z+5. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$z^{2}+2z+5=0$$

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 1 mō te a, te 2 mō te b, me te 5 mō te c i te ture pūrua.

$$z=\frac{-2±\sqrt{2^{2}-4\times 1\times 5}}{2}$$

Mahia ngā tātaitai.

$$z=\frac{-2±\sqrt{-16}}{2}$$

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

$$z\in \emptyset$$

Rārangitia ngā otinga katoa i kitea.

$$z=\frac{1}{2}$$