Quadratic Formator
Jichanganya na mchanganyiko wowote wa ax2 + bx + c = 0, kutia ndani mizizi tata.
Matokeo yanakuwa bora zaidi unapochapa.
Kuhusu kifaa hiki cha kupigia hesabu
This calculator solves a quadratic equation ax² + bx + c = 0 using the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. Enter the coefficients a, b and c and it returns both roots, the discriminant, the nature of the roots, the parabola's vertex and axis of symmetry, and the factored form, along with a plot of the curve.
The discriminant b² − 4ac decides everything: a positive value gives two distinct real roots, zero gives one repeated real root, and a negative value gives a pair of complex conjugate roots written with i. Take x² − 5x + 6 = 0 (the defaults, a = 1, b = −5, c = 6): the discriminant is 25 − 24 = 1, so there are two real roots, x = 3 and x = 2, the vertex is at (2.5, −0.25) with axis of symmetry x = 2.5, and the factored form is (x − 3)(x − 2). If a is 0 the equation is linear, not quadratic, and the formula does not apply.
Quadratics model projectile paths, areas, profit-maximizing prices and many optimization problems. The vertex gives the maximum or minimum point of the parabola, while the roots are where it crosses the x-axis.
Maswali yaliyoulizwa mara nyingi
Mtabiri huyo ananiambia nini?
Neno griint b2 kujali 4ac huamua mizizi: chanya humaanisha masuluhisho mawili halisi, sufuri humaanisha suluhisho moja la kurudia, na yasiyofaa humaanisha masuluhisho mawili tata.
Namna gani ikiwa sufuri ni sufuri?
Kisha mlingano huo ni wa trari, si wa hesabu, na michanganyiko ya quadatic haitumiki.
Ni nini matokeo ya parabola?
Ni wakati wa mabadiliko (h, k) ambapo mpindo hufikia upeo wake au mdogo zaidi. Chombo hiki kinakiripoti pamoja na mhimili wa upatano, mstari x = h.
Aina hiyo ya damu inaonyesha nini?
Mizizi inapokomaa, mlinganyo huo huandikwa upya íx kujali1) íx í2 kujali 5x + 6 = 0 (x kujali 3) jukx jundi 2).
Ni nini chanzo tata?
Wakati mtabiri anapoharibu mizizi yake ni jozi ya kaporove with the costelite olite, na kifaa hicho huiandika kwa namna hiyo.
Solve x² − 5x + 6 = 0.
Kionyeshi ni 1, ikitoa mizizi miwili halisi, x = 3 na x = 2 Étating emoct jope ionyeshwayo na kikoa hiki.
API bustanini hutumia kifaa hiki cha hesabu kutoka kwenye mfumo wa sheria
Ipigie simu kifaa hiki cha kupigia hesabu kama Junse É not doot toder. Chochote unachoacha kinatumia kiwango kilekile cha mwisho ambacho ukurasa huu haujakamilika; parameta isiyojulikana ni 400, si sufuri kimya kamwe. Soma habari kamili za API docs →
keyboard label
GET https://calculator.free/api/v1/quadratic-formula/curl
curl "https://calculator.free/api/v1/quadratic-formula/?a=1&b=-5&c=6"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/quadratic-formula/?" + new URLSearchParams({
"a": "1",
"b": "-5",
"c": "6"
}));
const data = await r.json();
console.log(data.results);Matokeo ni makadirio ya mwongozo wa ujumla, si wa kifedha, wa kitiba au wa kodi tu.