Kalkuleta Daidaito na Huɗu

Ƙa’ida

x = [−b ± √(b² − 4ac)] ÷ 2a. Discriminant D = b² − 4ac yana tantance nau’in tushen: D > 0 yana ba da real roots biyu daban, D = 0 yana ba da tushe ɗaya mai maimaituwa, D < 0 yana ba da complex roots biyu. Ƙimar x ta vertex ita ce x = −b ÷ 2a.

Misalin aiki

x² − 5x + 6 = 0: a = 1, b = −5, c = 6. Mai rarrabewa = (−5)² − 4 × 1 × 6 = 25 − 24 = 1. Tushen = [5 ± √1] ÷ 2, don haka x = 3 da x = 2. Duba: 3² − 15 + 6 = 0 da 2² − 10 + 6 = 0. Daidaito yana a x = 2.5.

Amfani da iyakoki

Nonzero a yana bayyana quadratic. Idan a sifili ne, shafin yana ba da rahoton yanayin daidaito na layi ko na dindindin. Sakamakon yawanci yana nuna lambobi masu mahimmanci na 12, suna ƙaruwa zuwa 17 don bambance tushen kusa. Ƙananan ƙima ko manyan ƙima suna amfani da bayanin kimiyya. Daidaiton shigarwar decimal har yanzu yana iyakance daidaito, musamman kusa da tushen da aka maimaita. Girman lambobi marasa tallafi suna nuna kuskure maimakon rashin iyaka ko sifili na ƙarya.

W. Kahan (2004), Qdrtcs

Sigar tsari: fd252bec1aa3 · An duba misali: 2026-10-31

FAQ

Me zai faru idan a sifili ne?

Sai a warware bx + c = 0. Idan b ba sifili bane, x = −c ÷ b. Idan b da c duka sifili ne, kowane ainihin x yana aiki; idan b sifili ne amma ba c ba ne, babu mafita.

Me mai rarrabewa ya gaya mini?

Ko tushen gaskiya ne kuma nawa ne: tabbatacce yana nufin asali guda biyu daban-daban na gaske, sifili yana nufin tushe ɗaya mai maimaitawa, korau yana nufin babu ainihin tushen - parabola ba ya taɓa ketare axis na x.

Menene tushen rikitarwa?

Lokacin da mai rarrabewa ya kasance korau, tushen ya ƙunshi i (tushen murabba'i na −1). Ga x² + 2x + 5 = 0 tushen sune −1 + 2i da −1 − 2i. Su ne mafita na gaske akan lambobi masu rikitarwa, kawai ba maki akan ainihin axis na x ba.

Me yasa tushen biyu?

Polynomial mai degree 2 yana da tushen biyu idan an ƙirga maimaituwar tushe. Suna iya zama tushe ɗaya da ya maimaitu ko kuma complex pair; idan an ƙirga maimaituwa, koyaushe guda biyu ne.

Shin ya kamata in ƙididdige maimakon haka?

Factoring yana da sauri lokacin da tushen ƙananan lambobi ne, kamar yadda yake a cikin misalin (x − 3)(x − 2). Tsarin koyaushe yana aiki, gami da lokacin da factoring ba a bayyane yake ba.

Shin vertex yana da mahimmanci?

Shi ne vertex na parabola: mafi ƙarancin ƙima idan a > 0, mafi girman ƙima idan a < 0. Ƙimar x ɗinsa tana daidai a tsakiyar real roots biyu idan suna akwai.

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