Qalabka tirakoobka
Xalka isku mid ah laba jibbaaran ax² + bx + c = 0, oo ay ku jiraan rooti adag.
Natiijooyinka cusbooneysiinta sida aad ku qorto.
Ku saabsan Kalkaaliyahan
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.
Su'aalaha badanaa la isweydiiyo
Maxaa kala sooc ah ii sheegi?
Dhibcaha b² - 4ac wuxuu go'aamiya dhir: Positive waxay ka dhigan tahay laba xal dhab ah, Zero waxay ka dhigan tahay xal isku laab ah, iyo Negative waxay ka dhigan tahay laba xal oo adag.
Maxaa haddii a waa zero?
Markaas isku midka waa line, ma squared, iyo qaabka squared ma aha mid ku habboon. Gaar ah qiimaha aan zero ah ee a.
Waa maxay vertex ee parabola?
Waa meesha wareega (h, k) halkaas oo curve gaadho ugu badnaan ama ugu yaraan. Qalabkani wuxuu ku wargeliyaa iyada oo la socda xagal isku mid ah, line x = h.
Maxaa ka dhigaysa qaabka factored muujiyaan?
Marka dhirtu ay run tahay, isku-duwaha waxaa loo qoraa a (x − r₁)(x − r₂). X² − 5x + 6 = 0 taas oo ah (x − 3)(x − 2).
Waa maxay jirridda adag?
Marka ay kala sooc waa xun dhirtu waa laba isku mid ah oo ± bi oo ay ku jiraan unit maahmaahday i, iyo qalabku u qoraa iyaga oo ka soo baxay qaabkaas.
Xal x² − 5x + 6 = 0.
The discriminant waa 1, siin laba dhir dhab ah, x = 3 iyo x = 2 — tusaale default muujiyay by xisaabinta this.
API — isticmaal xisaabinta ka code
Wici xisaabinta sida free JSON endpoint - key ma loo baahan yahay. Dib u soo dir qiimaha goobta hoos ku qoran sida parameters su'aal ama JSON. Wax kasta oo aad ka maqan tahay isticmaalaa default la mid ah ee boggani waa hore loo buuxiyey la; parameter aan la aqoon waa 400, marnaba ma aha zero maqan. Akhri dhammaan API xuquuqda →
Xarafka
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);Natiijooyinka waa tirakoobka loogu talagalay tilmaamaha guud oo keliya, maaha dhaqaale, caafimaad ama talo bixin canshuur.