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Tushen gaske na lissafin digiri na biyu

Wadanne ƙimomin x na gaske ne suke cika lissafinka ax² + bx + c = 0?

Shigar da ma’aunai uku. Lissafta diskriminant, yawan tushen gaske masu bambanci da ƙimominsu a jere.

Ma’aunanka

Rubuta lissafin a siffar ax² + bx + c = 0 kafin shigar da ma’aunansa. Riƙe alamominsu. Yi amfani da ƙimomi masu daidaituwa a cikin lissafin; ba a sauya raka’o’i. Shigar da gutsattsari a desimal, ba a/b ba.

Yadda ake samun kimantawa

D = b² − 4ac. Ga a ≠ 0: D < 0 yana nufin babu tushen gaske; D = 0 yana ba da tushen mai maimaituwa −b/(2a); D > 0 yana ba da (−b ± √D)/(2a). Ana jera sakamako daga ƙarami zuwa babba, ko da a yana da alamar ragewa. Ana buƙatar duk ma’aunai uku. Rarrabawa tana amfani da diskriminant kafin zagaye lamba.

ax² + bx + c = 0; a ≠ 0
D = b² − 4ac
x = (−b ± √D) ÷ (2a); D ≥ 0

Don lissafin skala guda na digiri na biyu mai ma’aunai na gaske kawai. Babu mafita ta layi a madadinsa, tushen hadaddun lambobi, rarrabawa zuwa abubuwan ninkawa ko fitar da dabara ta alamomi, jadawalin zane, daidaita lanƙwasa da bayanai, hasashen ma’aunai, kimanta rashin tabbas, tabbatar da aunawa, hasashen zahiri ko shawarar aminci. Shigar da lissafin ƙididdiga ba ya tabbatar da samfurin duniyar gaske.

Lissafin digiri na biyu da dabara ↗
Diskriminant da yawan tushen gaske ↗

Duba misalin da aka cika

Misalin da muka zaɓa: a = 2, b = −5, c = −3 yana ba da 2x² − 5x − 3 = 0. D = 25 + 24 = 49; tushen gaske su ne −0.5 da 3. Maye gurbin kowane ɗaya a lissafin yana ba da 0. Waɗannan ma’aunai ne na lissafi da aka zaɓa, ba ƙa’ida ko hasashen zahiri ba.

Ƙimomin da aka karɓa

Ma’aunin a
2
Ma’aunin b
-5
Dindindin c
-3

Shirya mataki na gaba

Yi amfani da kalkuleta na yau da kullum don wasu ayyukan lissafi dabam. Tabbatar an mayar da asalin lissafinka zuwa siffar da aka bayyana.

Kalkuleta na yau da kullum →