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

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

Whakaoti mō x

$$x=2$$

$$x=4$$

$$x=-3$$

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}-3x^{2}-10x+24 ki te x-2, kia riro ko x^{2}-x-12. Whakaotihia te whārite ina ōrite te hua ki te 0.

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

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 -1 mō te b, me te -12 mō te c i te ture pūrua.

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

Mahia ngā tātaitai.

$$x=\frac{1±7}{2}$$

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

$$x=-3 x=4$$

Rārangitia ngā otinga katoa i kitea.

$$x=2 x=-3 x=4$$