Àwọn Ìṣàmúlò-ètò

Ṣàfikún àwọn ìṣàmúlò-ètò kọ́ọ̀kan ax² + bx + c = 0, àti àwọn ìrísí-lẹ́tà ìṣàmúlò-ètò.

Aṣàfilọ́lẹ̀ akọkọ (x₁) —

Aṣàfilọ́lẹ̀ kẹtà (x₂) —

Discriminant (b² − 4ac) —

Àwọn ìṣàmúlò-ètò —

Àwọn ààyè-iṣẹ́ —

Àwọn ààyè-iṣẹ́ ìṣàfarawé —

Àwọn ìṣàmúlò-ètò —

Àwọn Àtòjọ-ẹ̀yàn àwọn ìṣàmúlò-ètò

Ńlà àwọn àwọn ààtò àtòjọ-ẹ̀yàn yìí?

Àkóónú ìṣàmúlò-ètò yìí

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.

Àwọn Àtòjọ-ẹ̀yàn

Kini ìṣàfarawé àwọn ìṣàmúlò-ètò sọ fún mi?

Iyatọ b² − 4ac n pinnu awọn roots: o tọka si awọn isẹpo meji gidi, satẹlaiti tọka si isẹpo kan ti o ṣẹlẹ, ati pe o tọka si awọn isẹpo meji ti o nira.

Ńjẹ́ tí a bá jẹ́ ìtàn?

Then the equation is linear, not quadratic, and the quadratic formula does not apply. Enter a non-zero value for a.

Àwọn ààyè-iṣẹ́ àwọn ààyè-iṣẹ́

Ó jẹ́ àwọn ààyè ìṣàfarawé (h, k) nínú àwọn ìsàlẹ̀-ilà náà tí wọ́n bá gbàjú àwọn ìsàlẹ̀-ilà tí a fẹ́. Àtòjọ-ẹ̀yàn yìí ń sọ̀rọ̀ ní pàtó àwọn ààyè tí a tì fi pamọ́, àwọn ààyè x = h.

Àwọn ìṣàmúlò-ètò àwọn ìṣàmúlò-ètò

Tí àwọn ìṣàmúlò-ètò jẹ́ òótọ́, àwọn ìṣàmúlò-ètò náà tí a kọ́ ní pàtó bí (x − r₁)(x − r₂). Fún x² − 5x + 6 = 0 ní (x − 3)(x − 2).

Kini àwọn ìrísí-lẹ́tà ìṣàfarawé?

Nigbati o ba jẹ pe aṣiṣe ti o ni ipalara, awọn akojọpọ jẹ awọn akojọpọ ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara ti o ni ipalara.

Ṣàfikún x² − 5x + 6 = 0.

The discriminant is 1, giving two real roots, x = 3 and x = 2 — the default example shown by this calculator.

API — ló àwọn ìṣàmúlò-ètò yìí láti inú ìṣàmúlò-ètò

Fi àwọn ìṣàmúlò-ètò yìí kọ̀ǹpútà yìí láti jẹ́ ààyè-iṣẹ́ JSON tí a tí fi pamọ́ - kò ní bọ́tìnì kan tí a fẹ́. Fi àwọn fálù ààyè-iṣẹ́ sílẹ̀ sí bí àwọn àwọn ìṣàmúlò-ètò àti JSON. Anything you omit uses the same default this page is pre-filled with; an unknown parameter is a 400, never a silent zero. Ka àwọn àkọlé API kíkún →

Àwọn Ààyè Ìjánu-ìṣàmúlò-ètò

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);

Results are estimates for general guidance only, not financial, medical or tax advice.

Àkóónú ìṣàmúlò-ètò yìí

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