Isixazululi se-equation
Kuxazululwe izinkinga ezihamba phambili, ezi-quadric kanye nezinhlelo ze-equations ngenyathelo ngalinye, mahhala kwi-inthanethi.
Iziphetho zivuselelwa uma ubhala.
Malunga nale khadi
An equation solver finds the values that satisfy an equation. This tool solves linear equations, quadratic equations (via the quadratic formula, including complex roots) and systems of two linear equations. Choose the type, enter the coefficients, and get the solution with the key working shown.
For a linear equation ax + b = 0 it simply rearranges to x = -b/a. For a quadratic ax² + bx + c = 0 it applies the quadratic formula, first computing the discriminant b² − 4ac: a positive discriminant gives two real roots, zero gives one repeated root, and a negative discriminant gives a pair of complex-conjugate roots which it reports rather than declaring "no solution". For a 2×2 system it solves the two lines simultaneously to find the single point where they cross.
For a worked example, solving x² − 5x + 6 = 0 gives a discriminant of 25 − 24 = 1, so the roots are x = (5 ± 1)/2, that is x = 3 and x = 2. By contrast x² + 1 = 0 has discriminant -4 and returns the complex roots x = i and x = -i. Students use it to check algebra homework, find where a parabola crosses the x-axis, or solve the pair of equations behind a word problem.
Imibuzo ebuzwa kaningi
Yini izinhlobo ze-equations ezingakwazi ukuxazulula?
I-equations eqondile (ax + b = 0), i-quadratics (ax² + bx + c = 0, kufaka phakathi izimpande ezinzima), kanye ne-2×2 system ye-equations eqondile.
Ingaba ibonisa izimpande ezinzima?
Yebo. Uma i-quadric ine-discriminant elahlekile, umxazululi ukhombisa izifunda ezimbili ezinzima ezixhunywe ngokuxhumeka, hhayi ukuthi akukho sinqumo.
Ngizoxazulula kanjani i-quadric njenge x² − 5x + 6 = 0?
Khetha uhlobo lwesikwere bese ufaka a = 1, b = -5, c = 6. Umxazululi ufaka ifomula yesikwere futhi ubuyisela x = 2 no x = 3, amaxabiso amabili akwenza uphawu lwesikwere kube yi-zero.
Yini i-discriminant nokuthi kungani ibalulekile?
I-discriminant yi-b² - 4ac. Uma i positive kunezinkolelo ezimbili ezingokoqobo, uma i zero kunezinkolelo ezimbili eziphindayo, futhi uma i negative izinkolelo ziyi-conjugate pair enzima. Umxazululi usebenzisa lokhu ukucabanga ukuthi iyiphi inkinga esebenza.
Ngizoxazulula kanjani i-system ye-equations ezimbili?
Khetha uhlobo lwendlela 2×2 bese ufaka izilinganiso zezinto ezimbili ezilinganayo. Umxazululi uthola indawo eyodwa (x, y) lapho imigqa emibini ihlangana khona, noma utshela lapho zifana futhi azikho ukungqubuzana.
Yini oyenzayo le divayisi ehlukile ku-calculator yodweba?
Isixazululi se-equation sibuyisela izindleko ezifanele zesinqumo nge-algorithm. I-calculator eshicilela izithombe izoba ne-curves ukuze ubone izitshalo njenge-x-axis crossings noma ukungqubuzana kwama-graphs amabili.
Izibalo ziyisilinganiso esisetshenziswa ukuqondisa kuphela, hhayi ukucebisa ngezimali, ukwelashwa noma ukukhokha.