Ukuxazulula izibalo zequadratic

Isibalo sequadratic isibalo sezibalo, ngokuvamile esibukeka kanje:

ax² + bx + c = 0

Leli i-oda lesibili le-polynomial elinama-coefficient angu-3:

• a - i-coefficient ephezulu (yokuqala), akufanele ilingane no-0;
• b - isilinganiso (yesibili) coefficient;
• c iyisici samahhala.

Isixazululo se-quadratic equation ukuthola izinombolo ezimbili (izimpande zayo) - x₁ kanye x₂.

Ifomula yokubala izimpande

Ukuthola izimpande ze-quadratic equation, ifomula isetshenziswa:

Isisho esingaphakathi kwempande yesikwele sibizwa ukubandlulula futhi imakwe ngohlamvu D (noma Δ):

D = b² - 4ac

Ngale ndlela, Ifomula yokubala izimpande ingamelwa ngezindlela ezahlukene:

1 Uma D > 0, isibalo sinezimpande ezi-2:

2 Uma D = 0, isibalo sinempande eyodwa kuphela:

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

Izixazululo zezibalo ze-quadratic

Isibonelo se-1

3x² 5 +x + 2 = 0

Isinqumo:

a = 3, b = 5, c = 2

x₁ = (-5 + 1) / 6 = -4/6 = -2/3

x₂ = (-5 – 1) / 6 = -6/6 = -1

Isibonelo se-2

3x² - 6x + 3 = 0

Isinqumo:

a = 3, b = -6, c = 3

x₁ = x₂ = 1

Isibonelo se-3

x² 2 +x + 5 = 0

Isinqumo:

a = 1, b = 2, c = 5

Kulokhu, azikho izimpande zangempela, futhi isisombululo izinombolo eziyinkimbinkimbi:

x₁ = -1 + 2i

x₂ = -1 – 2i

Igrafu yomsebenzi we-quadratic

Igrafu yomsebenzi we-quadratic ngu umfanekiso.

f(x) = ax² + b x + c

• Izimpande ze-quadratic equation amaphuzu okuhlangana kwe-parabola ne-abscissa axis (X).
• Uma kukhona impande eyodwa kuphela, i-parabola ithinta i-eksisi ngesikhathi esisodwa ngaphandle kokuyiwela.
• Uma kungekho izimpande zangempela (ukuba khona kweziyinkimbinkimbi), igrafu ene-eksisi X ayithinti.