Mene ne zeros da kuma yadda za a gano su

Mene ne zeros? Amsar ne quite sauki - shi ne mai ilmin lissafi lokaci, da wanda ake nufi cikin yankin da aka ba aiki, inda da darajar ne sifili. Zeros kuma ake kira tushen da lissafi. A mafi sauki hanyar bayyana abin da zeros, wasu sauki misalai.

misalai

Ka yi la'akari da sauki lissafi y = x + 3. Tun da ayyuka ba kome - tamanin da shawara, wadda yi tsiwirwirinsu a sifili, muka musanyata 0 cikin gefen hagu na lissafi:

0 = x + 3.

x = -3.

A wannan yanayin ne da ake so -3 sifili. Domin wannan aiki, akwai daya kawai tushen na lissafi, amma shi ne ba ko da yaushe.

La'akari da wani misali:

y = x ² -9.

Muka musanya 0 cikin gefen hagu na lissafi, kamar yadda a baya misali:

0 = x ² -9.

X ² = -9.

Babu shakka, a cikin wannan yanayin, da zeros zai zama biyu x = 3 da x = -3. Idan a cikin lissafi ya da hujja na uku mataki, uku zeros kamar. Za ka iya zana wani sauki ƙarasawa da cewa, yawan Tushen wata polynomial ne matsakaicin mataki na ta shaida a lissafi. Duk da haka, da yawa ayyuka, kamar y = x ^3, ze musanta wannan sanarwa. Dabaru da kowa hankali bayar da shawarar cewa wannan aiki ne kawai daya sifili - batun da x = 0. Amma a gaskiya, da tushen da uku, duk suna da kamar guda. Idan muka warware lissafi a wani hadadden tsari, shi ya zama a bayyane yake. x = 0 cikin wannan harka, tushen da riɓanya 3. A baya misali, zeros ba daidaita, domin wanda ya multiplicity.

kafiya algorithm

Daga wadannan misalai nuna yadda za a ƙayyade da zeros. A algorithm ne ko da yaushe wannan:

1. Record aiki.
2. Canza y ko f (x) = 0.
3. Warware sakamakon lissafi.

Haduwar karshe ma'ana dogara a kan mataki na lissafi na shaida. A shawarar da babban mataki na lissafi ne musamman da muhimmanci a tuna cewa yawan tushen da lissafi ne daidai da matsakaicin mataki na shaida. Wannan Gaskiya ne, don trigonometric lissafai, inda biyu division rabo da ba tare da ko cosine take kaiwa zuwa asarar asalinsu.

A lissafai na sabani mataki ne mafi sauki warware ta Horner, wanda aka tsara, musamman, domin gano zeros na wani sabani polynomial.

Tamanin da zeros iya zama ko dai korau ko tabbatacce, real ko kwance a cikin hadaddun jirgin sama, guda ko mahara. Ko da tushen bazai. Alal misali, aikin y = 8 ba zai samu sifili ga wani x, saboda shi ba ya dogara ne a kan wannan m.

A lissafi y = x ² -16 yana da biyu Tushen, da kuma duka ƙarya a cikin hadaddun jirgin sama: x = 4і _1, x ₂ = -4і.

kowa kuskure

A na kowa kuskure da cewa dalibai har yanzu ba su fitar da siffa mai yawa game da abin da yake zeros - An maye gurbinsu da sifili shaida (s) da kuma ba da darajar (y) aiki. Su amincewa sa a cikin lissafi x = 0 kuma, a wannan hasashe, suna a. Amma wannan shi ne daidai ba ne m.

Wani kuskure, kamar yadda aka ambata riga, da rage daga cikin ba tare da ko cosine a trigonometric lissafai, saboda abin da aka rasa, da kuma daya ko fiye zeros. Wannan ba ya nufin cewa wadannan lissafai ba zai iya yanka wani abu, kawai a lokacin da kara lissafin dole ne ya yi la'akari da wadannan "rasa" dalilai.

zana wakilci

Fahimci abin da zeros, za ka iya amfani da ilmin lissafi da shirye-shirye kamar Maple. Yana yiwuwa a yi wani jadawali na nuna da ake so yawan maki da kuma so sikelin. Wadanda maki a da jadawali crosses da x-axis ne ake bukata zeros. Wannan shi ne daya daga cikin gaggawa hanyoyi na gano tushen da wani polynomial, musamman idan ta ya fi yadda na uku domin. Saboda haka idan akwai bukatar a kai a kai cika ilmin lissafi lissafin, a sami tushen polynomials na sabani iko, gina jadawalai, Maple ko kama da shirin ne kawai ba makawa ga aiwatar da tabbaci daga cikin lissafin.