Whakaoti i te m^4+3m^2-4

$${ m }^{ 4 } +3 { m }^{ 2 } -4$$

Tauwehe

$$\left(m-1\right)\left(m+1\right)\left(m^{2}+4\right)$$

Ngā Upane Otinga

Kia tauwehea ai te kīanga, me whakaoti te whārite ina ōrite ki te 0.

$$m^{4}+3m^{2}-4=0$$

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 -4, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±4,±2,±1$$

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.

$$m=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te m-k o te pūrau mō ia pūtake k. Whakawehea te m^{4}+3m^{2}-4 ki te m-1, kia riro ko m^{3}+m^{2}+4m+4. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.

$$m^{3}+m^{2}+4m+4=0$$

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 4, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±4,±2,±1$$

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.

$$m=-1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te m-k o te pūrau mō ia pūtake k. Whakawehea te m^{3}+m^{2}+4m+4 ki te m+1, kia riro ko m^{2}+4. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.

$$m^{2}+4=0$$

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 0 mō te b, me te 4 mō te c i te ture pūrua.

$$m=\frac{0±\sqrt{0^{2}-4\times 1\times 4}}{2}$$

Mahia ngā tātaitai.

$$m=\frac{0±\sqrt{-16}}{2}$$

Kāore te pūrau m^{2}+4 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$m^{2}+4$$

Me tuhi anō te kīanga whakatauwehe mā ngā pūtake i riro.

$$\left(m-1\right)\left(m+1\right)\left(m^{2}+4\right)$$

Aromātai

$$m^{4}+3m^{2}-4$$