Kev daws teeb meem quadratic equations

Quadratic equation yog ib tug lej sib npaug, uas feem ntau zoo li no:

ax² + bx + c = 0

Qhov no yog qhov kev txiav txim thib ob polynomial nrog 3 coefficients:

• a - laus (thawj) coefficient, yuav tsum tsis txhob sib npaug rau 0;
• b - nruab nrab (thib ob) coefficient;
• c yog ib qho khoom pub dawb.

Kev daws rau ib qho kev sib npaug plaub yog nrhiav ob tus lej (nws cov hauv paus hniav) - x₁ thiab x₂.

Cov mis rau xam cov hauv paus hniav

Yuav kom nrhiav tau cov hauv paus hniav ntawm ib qho kev sib npaug quadratic, cov qauv siv:

Cov lus qhia hauv lub hauv paus square yog hu ua xaiv neeg thiab cim nrog tsab ntawv D (los yog Δ):

D = b² - 4ac

Txoj kev no, Cov mis rau xam cov hauv paus hniav tuaj yeem sawv cev rau ntau txoj hauv kev:

1 D > 0, qhov sib npaug muaj 2 lub hauv paus:

2 D = 0, qhov sib npaug tsuas muaj ib lub hauv paus:

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

Cov kev daws teeb meem ntawm quadratic equations

Piv txwv li 1

3x² + 5x 2 = 0 TZS

Kev txiav txim siab:

a = 3, b = 5, c = 2

x₁ = (-5 + 1) / 6 = -4/6 = -2/3

x₂ = (-5 – 1) / 6 = -6/6 = -1

Piv txwv li 2

3x² - 6x 3 = 0 TZS

Kev txiav txim siab:

a = 3, b = -6, c = 3

x₁ = x₂ = 1

Piv txwv li 3

x² + 2x 5 = 0 TZS

Kev txiav txim siab:

a = 1, b = 2, c = 5

Hauv qhov no, tsis muaj cov hauv paus hniav tiag tiag, thiab cov kev daws teeb meem yog cov lej:

x₁ = -1 + 2i

x₂ = -1-2i

Graph ntawm ib qho kev ua haujlwm quadratic

Daim duab ntawm lub quadratic muaj nuj nqi yog ib zaj lus piv txwv.

f(x) = ax² bx + c

• Cov hauv paus hniav ntawm ib qho kev sib npaug quadratic yog cov ntsiab lus ntawm kev sib tshuam ntawm parabola nrog abscissa axis (X).
• Yog tias tsuas muaj ib lub hauv paus, lub parabola kov lub axis ntawm ib qho chaw tsis hla nws.
• Nyob rau hauv tsis muaj cov hauv paus hniav tiag tiag (lub xub ntiag ntawm complex ones), ib daim duab nrog ib tug axis X tsis kov.