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Ngā Raru Ōrite mai i te Rapu Tukutuku

Tohaina

2x^{4}-5x^{3}+4x^{2}-5x+2=0
Kia tauwehea ai te kīanga, me whakaoti te whārite ina ōrite ki te 0.
±1,±2,±\frac{1}{2}
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 2, ā, ka wehea e q te whakarea arahanga 2. Whakarārangitia ngā kaitono katoa \frac{p}{q}.
x=2
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.
2x^{3}-x^{2}+2x-1=0
Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te 2x^{4}-5x^{3}+4x^{2}-5x+2 ki te x-2, kia riro ko 2x^{3}-x^{2}+2x-1. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.
±\frac{1}{2},±1
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 -1, ā, ka wehea e q te whakarea arahanga 2. Whakarārangitia ngā kaitono katoa \frac{p}{q}.
x=\frac{1}{2}
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}+1=0
Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te 2x^{3}-x^{2}+2x-1 ki te 2\left(x-\frac{1}{2}\right)=2x-1, kia riro ko x^{2}+1. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.
x=\frac{0±\sqrt{0^{2}-4\times 1\times 1}}{2}
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 1 mō te c i te ture pūrua.
x=\frac{0±\sqrt{-4}}{2}
Mahia ngā tātaitai.
x^{2}+1
Kāore te pūrau x^{2}+1 i whakatauwehea i te mea kāhore ōna pūtake whakahau.
\left(x-2\right)\left(2x-1\right)\left(x^{2}+1\right)
Me tuhi anō te kīanga whakatauwehe mā ngā pūtake i riro.