Whakaoti i te x^4-105x^2-1936

$${ x }^{ 4 } -105 { x }^{ 2 } -1936$$

Tauwehe

$$\left(x-11\right)\left(x+11\right)\left(x^{2}+16\right)$$

Ngā Upane Otinga

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

$$x^{4}-105x^{2}-1936=0$$

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 -1936, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±1936,±968,±484,±242,±176,±121,±88,±44,±22,±16,±11,±8,±4,±2,±1$$

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.

$$x=11$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{4}-105x^{2}-1936 ki te x-11, kia riro ko x^{3}+11x^{2}+16x+176. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.

$$x^{3}+11x^{2}+16x+176=0$$

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

$$±176,±88,±44,±22,±16,±11,±8,±4,±2,±1$$

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.

$$x=-11$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}+11x^{2}+16x+176 ki te x+11, kia riro ko x^{2}+16. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.

$$x^{2}+16=0$$

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 16 mō te c i te ture pūrua.

$$x=\frac{0±\sqrt{0^{2}-4\times 1\times 16}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{0±\sqrt{-64}}{2}$$

Kāore te pūrau x^{2}+16 i whakatauwehea i te mea kāhore ōna pūtake whakahau.

$$x^{2}+16$$

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

$$\left(x-11\right)\left(x+11\right)\left(x^{2}+16\right)$$

Aromātai

$$x^{4}-105x^{2}-1936$$