Ho rarolla quadratic equations

Quadratic equation ke lipalo tsa lipalo, tseo ka kakaretso li shebahalang tjena:

ax² + bx + c = 0

Ena ke taelo ea bobeli ea polynomial e nang le li-coefficients tse 3:

• a - coefficient e kholo (ea pele), ha ea lokela ho lekana le 0;
• b - karolelano (ea bobeli) coefficient;
• c ke ntho e sa lefelloeng.

Tharollo ea quadratic equation ke ho fumana linomoro tse peli (metso ea eona) - x₁ le x₂.

Foromo ea ho bala metso

Ho fumana metso ea quadratic equation, foromo e sebelisoa:

Polelo e ka hare ho motso oa lisekoere e bitsoa khethollo mme e tshwailwe ka tlhaku D (kapa Δ):

D = b² - 4ac

Ka tsela ena, Foromo ea ho bala metso e ka emeloa ka litsela tse fapaneng:

1. Haeba D > 0, equation e na le metso e 2:

2. Haeba D = 0, equation e na le motso o le mong feela:

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

Litharollo tsa quadratic equations

Mohlala 1

3x² + 5x + 2 = 0

Qeto:

a = 3, b = 5, c = 2

x₁ = (-5 + 1) / 6 = -4/6 = -2/3

x₂ = (-5 – 1) / 6 = -6/6 = -1

Mohlala 2

3x² - 6x + 3 = 0

Qeto:

a = 3, b = -6, c = 3

x₁ = x₂ = 1

Mohlala 3

x² + 2x + 5 = 0

Qeto:

a = 1, b = 2, c = 5

Tabeng ena, ha ho na metso ea 'nete,' me tharollo ke linomoro tse rarahaneng:

x₁ = -1 + 2i

x₂ = -1 – 2i

Kerafo ea tšebetso ea quadratic

Kerafo ea mosebetsi oa quadratic ke papiso.

f(x) = ax² + b x + c

• Metso ea quadratic equation ke lintlha tsa mateano a parabola le abscissa axis. (X).
• Haeba ho na le motso o le mong feela, parabola e ama axis ka nako e le 'ngoe ntle le ho e tšela.
• Ha ho se na metso ea 'nete (ho ba teng ha tse rarahaneng), kerafo e nang le axis X ha e ame.