Calculator
Dozie ọbụla kwaarịtik equation ax² + bx + c = 0, gụnyere pọ̀pụ̀lị̀ rị́ị̀k̀ọ̀tụ̀ọ̀tụ̀.
Nhọrọ ndị ahụ ga-akpụzi mgbe ị na-etipụta.
N'ihe banyere calculator a
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.
Ajụjụ ndị a na-ajụkarị
Gịnị ka ngwe-eziga-m na-agwa m?
The discriminant b² − 4ac decides the roots: positive means two real solutions, zero means one repeated solution, and negative means two complex solutions.
Gịnị ma ọ bụrụ na a bụ sẽọ̀rọ̀?
Mgbe ahụ, equation bụ linear, ọ bụghị quadratic, nakwa quadratic formula anaghị arụ ọrụ. Tinye uru na-enweghị sẽọ̀rọ̀ maka a.
Gịnị bụ vertex nke paraboolu ahụ?
Ọ bụ ntọala ntụgharị (h, k) ebe kurva na-abịarute n'ụdị kachasị ma ọ bụ nke kacha nta. Tulee a na-egosipụta ya n'otu n'otu na axis nke symmetry, laịị x = h.
Gịnị ka ọbụna usoroiheomume na-egosi?
Mgbe rịti ahụ bụ eziokwu, equation ahụ a ga-edegharị ya dịka a(x − r₁)(x − r₂). Maka x² − 5x + 6 = 0 nke bụ (x − 3)(x − 2).
Gịnị bụ urui ndị dị mfe?
Mgbe a na-atụgharị ihe ndị dị n'ime ihe ahụ ka ha bụrụ ihe dị iche iche, a na-atụgharị ihe ndị dị n'ime ihe ahụ ka ha bụrụ ihe dị iche iche.
Dozie x² − 5x + 6 = 0.
1 bụ 1, na-enye urui abụọ, x = 3 na x = 2 - dìfọ́ọ̀ltụ̀ ihenhọrọ ahụ egosipụtara site na kalkulata a.
API — jiri kaadị a site na kóòdù
Kpọọ kalkulata a dịka ebe ngwụcha JSON n'efu - enweghị kii achọrọ. Ziga valiu ebe ahụ n'okpuru dịka paramita ajụjụ mọọbụ JSON. Ihe ọbụla ị na-ewepụ na-eji dìfọ́ọ̀ltụ̀ nke a na-edebe ihuakwụkwọ a na ya; parameter a na-amaghị bụ 400, ọ dịghị sẽọ̀rọ̀. Gụọ ngwe ndị ahụ niile →
Ebemkpofuozi
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);Ihe a na-ahụta bụ n'ihi nlekọta n'ozuzu ya, ọ bụghị nlekọta ego, ọgwụ ma ọ bụ nlekọta ego.