Video: Lub rational root theorem hais li cas?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Rational root theorem . Cov theorem hais uas cwb kev xav x = p/q, sau nyob rau hauv cov nqe lus qis tshaj kom p thiab q yog cov tseem ceeb, txaus siab: p yog ib qho tseem ceeb ntawm lub sij hawm tas li a0, thiab.
Hais txog qhov no, dab tsi yog lub hauv paus rational?
Cov Cov hauv paus ntsiab lus Test (tseem hu ua Rational Zeros Theorem) tso cai rau peb nrhiav tau tag nrho tau rational cag ntawm ib tug polynomial. Hauv lwm lo lus, yog tias peb hloov tus lej rau hauv lub polynomial P (x) Plef(x ight) P(x) thiab tau xoom, 0, nws txhais tau hais tias tus nqi nkag yog ib qho. hauv paus ntawm kev ua haujlwm.
Tsis tas li ntawd, dab tsi yog qhov tseem ceeb hauv paus theorem? Cov integral root theorem qhia peb tias yog ib tug polynomial nrog tus lej coefficients muaj ib tug ua coefficient ntawm thiab ib tug trailing coefficient ntawm, ces tsuas yog ua tau yam tseem ceeb ntawm daim ntawv, qhov twg yog ib tug tus lej , yog cov uas yog qhov tseem ceeb ntawm.
Ib yam li ntawd ib tug yuav nug, dab tsi yog qhov radical cag theorem?
yog rational, Conjugate Radical Roots theorem hais tias yog qhov sib npaug p(x)=0 muaj a hauv paus ntawm daim ntawv x = s + t√u qhov twg √u yog rational, ces qhov sib npaug yuav tsum muaj cov conjugate radical , x=s−t√u, as a hauv paus.
Puas yog cov hauv paus hauv paus rational lej?
Nws yog ib tus lej uas tsis tuaj yeem sau ua piv txwv ntawm ob tus lej (lossis tsis tuaj yeem hais ua ib feem). Tsuas yog cov cov hauv paus plaub hau ntawm tus lej square yog kev xav . Ib yam li Pi (π) yog qhov tsis sib haum xeeb tus lej vim nws tsis tuaj yeem qhia tau tias yog ib feem ntawm ob qho tag nrho tus lej thiab nws tsis muaj qhov tseeb lej sib npaug.
Pom zoo:
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Peb hais txog kev txwv vim nws yuav ua rau qhov sib npaug tsis tau txhais hauv qee qhov txiaj ntsig ntawm x. Qhov kev txwv ntau tshaj plaws rau cov lus qhia muaj nuj nqis yog N / 0. Qhov no txhais tau tias txhua tus lej muab faib los ntawm xoom tsis tau txhais. Piv txwv li, rau txoj haujlwm f(x) = 6/x², thaum koj hloov x = 0, nws yuav ua rau 6/0 uas tsis tau txhais
Lub ntsiab lus ntawm lub hauv paus rational yog dab tsi?
Rational Roots Test. Qhov Kev Ntsuas Ntsuas Qhov Ntsuas (tseem hu ua Rational Zeros Theorem) tso cai rau peb pom txhua qhov ua tau zoo ntawm cov hauv paus ntsiab lus ntawm polynomial. Hauv lwm lo lus, yog tias peb hloov tus lej mus rau hauv lub polynomial P (x) Plef(x ight) P(x) thiab tau xoom, 0, nws txhais tau hais tias tus nqi nkag yog lub hauv paus ntawm txoj haujlwm
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