Kwardal Formul Kalkülatory
Solve any quadratic equation ax² + bx + c = 0, including complex roots.
Netijeler ýazýan wagtyň täzelener.
Bu hasapçy hakda
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.
Köp soralýan soraglar
Näme diýýär?
B² − 4ac diskriminant kökleri kesgitleýär: pozitiw iki aňrybaş çözgüt, sıfır bir gaýtalanan çözgüt we negatiw iki kompleks çözgüt.
Eger a sıfryň içinde bolsa näme?
Eger deňleşik dörtlü däl, dörtlü formulalar ulanylmaz. a üçin bir sıfryň ýok umumyny giriz.
Parabolanyň çepesi näme?
Bu egriň iň köpe ýa-da iň azyna ýeten dönme nokady (h, k)dir. Bu esbap ony symmetriýa egri bilen, x = h hat bilen habar berýär.
Faýllar
Eger kökler küýze bolsa, deňleşik a(x − r₁)(x − r₂) ýaly tekrar ýazylýar. x² − 5x + 6 = 0 üçin bu (x − 3)(x − 2)
Kompýuter
Diskriminant menfiy bolsa kökler hayal birligi i bilen bir a ± bi konjugat çiftdir we esbap olary şol şekilde ýazýar.
x2 - 5x + 6 = 0 çöz
Diskriminant 1, iki akyly köki berýän, x = 3 we x = 2 - bu kalkulýator tarapyndan görkezlen öň bellenen mysal.
API — bu hasapçyny koddan ullan
Bu hasapçyny boş JSON ahtar noktasy hökmünde çagyr - açar gerek däl. Aşakdaky meýdança mykdarlaryny soragyň parametrleri ýa-da JSON hökmünde iber. Siziň goýmaýan hernäňiz şu sahypanyň öň bellenen öň bellenenini ulanýar; namydar parametr 400, hiç wagt sessiz sıfır däl. Eňlisçe senedleri oka →
Endpoint
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);Netijeler diňe umumy ýardam üçin hasaplanypdyr, maliýe, saglyk ýa-da salgyt maslahaty üçin däl.