Kuthetsa ma quadratic equations

Quadratic equation ndi masamu equation, yomwe nthawi zambiri imawoneka motere:

ax² + bx + c = 0

Ili ndi dongosolo lachiwiri la polynomial lomwe lili ndi ma coefficients atatu:

• a - coefficient wamkulu (woyamba), sayenera kukhala wofanana ndi 0;
• b - pafupifupi (wachiwiri) coefficient;
• c ndi chinthu chaulere.

Yankho la quadratic equation ndikupeza manambala awiri (mizu yake) - x₁ ndi x₂.

Fomula yowerengera mizu

Kuti mupeze mizu ya quadratic equation, njirayi imagwiritsidwa ntchito:

Mawu omwe ali mkati mwa square root amatchedwa tsankho ndipo chalembedwa ndi chilembo D (kapena Δ):

D = b² - 4ac

Mwa njira iyi, Njira yowerengera mizu imatha kuyimiridwa m'njira zosiyanasiyana:

1. Ngati D > 0, equation ili ndi mizu iwiri:

2. Ngati D = 0, equation ili ndi muzu umodzi wokha:

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

Mayankho a quadratic equations

Mwachitsanzo 1

3x² + 5x + 2 = 0

Kusankha:

a = 3, b = 5, c = 2

x₁ = (-5 + 1) / 6 = -4/6 = -2/3

x₂ = (-5 – 1) / 6 = -6/6 = -1

Mwachitsanzo 2

3x² - 6x + 3 = 0

Kusankha:

a = 3, b = -6, c = 3

x₁ = x₂ = 1

Mwachitsanzo 3

x² + 2x + 5 = 0

Kusankha:

a = 1, b = 2, c = 5

Pankhaniyi, palibe mizu yeniyeni, ndipo yankho lake ndi manambala ovuta:

x₁ = -1 + 2i

x₂ = -1 - 2i

Chithunzi cha quadratic function

Chithunzi cha ntchito ya quadratic ndi fanizo.

f(x) = ax² + b x + c

• Mizu ya quadratic equation ndi mfundo za mphambano ya parabola ndi abscissa axis. (X).
• Ngati pali muzu umodzi wokha, parabola imakhudza olamulira nthawi imodzi popanda kuwoloka.
• Popanda mizu yeniyeni (kukhalapo kwa zovuta), graph yokhala ndi axis X sichikhudza.