Whakaoti i te x^3-10x^2+28x-24=0

$$x ^ { 3 } - 10 x ^ { 2 } + 28 x - 24 = 0$$

Whakaoti mō x

$$x=2$$

$$x=6$$

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 -24, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±24,±12,±8,±6,±4,±3,±2,±1$$

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.

$$x=2$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}-10x^{2}+28x-24 ki te x-2, kia riro ko x^{2}-8x+12. Whakaotihia te whārite ina ōrite te hua ki te 0.

$$x^{2}-8x+12=0$$

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 -8 mō te b, me te 12 mō te c i te ture pūrua.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 1\times 12}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{8±4}{2}$$

Whakaotia te whārite x^{2}-8x+12=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=2 x=6$$

Rārangitia ngā otinga katoa i kitea.

$$x=2 x=6$$