Kugadzirisa quadratic equations

Quadratic equation is a mathematical equation, iyo inowanzoita seizvi:

ax² + bx + c = 0

Iyi ndiyo yechipiri kurongeka polynomial ine 3 coefficients:

• a - mukuru (yekutanga) coefficient, haifanirwe kuenzana ne0;
• b - avhareji (yechipiri) coefficient;
• c chinhu chemahara.

Mhinduro kuquadratic equation ndeyekutsvaga manhamba maviri (midzi yawo) – x₁ uye x₂.

Formula yekuverenga midzi

Kuti uwane midzi yequadratic equation, fomula inoshandiswa:

Chirevo chemukati cheskweya midzi chinonzi rusarura uye yakanyorwa netsamba D (kana Δ):

D = b² - 4ac

Nenzira iyi, Iyo formula yekuverenga midzi inogona kumiririrwa nenzira dzakasiyana:

1. Kana D > 0, iyo equation ine midzi miviri:

2. Kana D = 0, iyo equation ine mudzi mumwe chete:

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

Mhinduro dze quadratic equations

muenzaniso 1

3x² + 5x +2 = 0

Sarudzo:

a = 3, b = 5, c = 2

x₁ = (-5 + 1) / 6 = -4/6 = -2/3

x₂ = (-5 – 1) / 6 = -6/6 = -1

muenzaniso 2

3x² - 6x +3 = 0

Sarudzo:

a = 3, b = -6, c = 3

x₁ = x₂ = 1

muenzaniso 3

x² + 2x +5 = 0

Sarudzo:

a = 1, b = 2, c = 5

Muchiitiko ichi, hapana midzi chaiyo, uye mhinduro inhamba dzakaoma:

x₁ = -1 + 2i

x₂ = -1 – 2i

Grafu ye quadratic function

Girafu ye quadratic function ndeye mufananidzo.

f(x) = ax² + b x + c

• Midzi yequadratic equation ndiwo mapoinzi ekuyambuka kweparabola neabscissa axis. (X).
• Kana paine mudzi mumwe chete, parabola inobata axis pane imwe nguva pasina kuyambuka.
• Mukusavapo kwemidzi chaiyo (kuvapo kwezvakaoma), girafu ine axis X haabate.