Magance ma'auni huɗu

Matsakaicin ma'auni lissafin lissafi ne, wanda gabaɗaya yayi kama da haka:

ax² + bx + c = 0

Wannan tsari ne na biyu mai yawa tare da ƙididdiga guda uku:

• a - babban (na farko) ƙididdiga, bai kamata ya zama daidai da 0 ba;
• b - matsakaici (na biyu) ƙididdiga;
• c sigar kyauta ce.

Maganin ma'auni guda huɗu shine nemo lambobi biyu (tushensa) - x₁ kuma x₂.

Formula don kirga tushen

Don nemo tushen ma'auni huɗu, ana amfani da dabarar:

Ana kiran magana a cikin tushen murabba'in m kuma an yi masa alama da harafin D (ko Δ):

D = b² - 4ac

Ta wannan hanyar, Ƙididdigar ƙididdiga na tushen za a iya wakilta ta hanyoyi daban-daban:

1 D > 0, lissafin yana da tushen guda 2:

2 D = 0, ma'auni yana da tushe ɗaya kawai:

3 D <0, вещественных корней нет, но есть комплексные:

Maganganun ma'asumai huɗu

Misali 1

3x² + 5x +2 = 0

Yanke shawara:

a = 3, b = 5, c = 2

x₁ = (-5 + 1) / 6 = -4/6 = -2/3

x₂ = (-5 - 1) / 6 = -6/6 = -1

Misali 2

3x² - 6x +3 = 0

Yanke shawara:

a = 3, b = -6, c = 3

x₁ = x₂ = 1

Misali 3

x² + 2x +5 = 0

Yanke shawara:

a = 1, b = 2, c = 5

A wannan yanayin, babu ainihin tushen, kuma mafita shine lambobi masu rikitarwa:

x₁ = -1 + 2i

x₂ = -1 - 2i

Hotunan aikin quadratic

Jadawalin aikin quadratic shine misali.

f(x) = ax² bx+c

• Tushen ma'auni huɗun su ne wuraren mahaɗar parabola tare da abscissa axis. (X).
• Idan tushen guda ɗaya ne, parabola ta taɓa axis a lokaci ɗaya ba tare da haye shi ba.
• Idan babu tushen asali (kasancewar hadaddun), jadawali tare da axis X baya tabawa.