Quadratic Formula Calculator kya solve karta hai?

Ye ax² + bx + c = 0 form ki koi bhi equation solve karta hai, x = (−b ± √(b² − 4ac)) / 2a use karke x ke dono values deta hai, saath hi discriminant aur parabola ka vertex bhi.

Discriminant kya hota hai aur ye kyun important hai?

Discriminant b² − 4ac hota hai. Positive value ka matlab do alag real roots, zero ka matlab ek repeated real root, aur negative value ka matlab dono roots complex conjugate hain.

Complex roots ka format kaisa hota hai?

Jab discriminant negative hota hai, Quadratic Formula Calculator pair ko a+bi aur a−bi likhta hai, aur agar real part zero ho aur imaginary coefficient 1 ho to sirf i ya −i tak simplify kar deta hai.

Calculator a = 0 ko kyun reject karta hai?

Agar a 0 hai to x² term hi khatam ho jaata hai aur equation linear (bx + c = 0) ban jaati hai, jo quadratic nahi hai — calculator zero se divide karne ke bajaye error dikhata hai.

Roots ke saath dikhaya gaya vertex value kya hai?

Ye parabola y = ax² + bx + c ka vertex (x, y) hai, jo x = −b / 2a par calculate hota hai. Ye parabola ka minimum ya maximum point hota hai, graph banane mein useful.

Kya is calculator ka use karte waqt meri equation kahin bhejii jaati hai?

Nahi. Quadratic Formula Calculator har result aapke browser mein hi calculate karta hai — jo coefficients aap daalte hain wo kabhi ArrayKit par upload nahi hote.

Quadratic Formula Calculator Online

ax² + bx + c = 0 ko real ya complex roots ke saath solve karein, discriminant aur vertex step-by-step dikhte hain. Aapke numbers aapke device par hi rehte hain.

Quadratic Formula Calculator poori tarah aapke browser mein chalta hai. Jo coefficients aap daalte hain aur jo roots ye calculate karta hai, wo kabhi aapke device se bahar nahi jaate.

Factor Calculator Kholein

Quadratic Formula Calculator ke baare mein

Quadratic Formula Calculator ax² + bx + c = 0 form ki koi bhi equation solve karta hai aur turant dono roots deta hai, chahe wo real ho ya complex. Teen coefficients a, b, aur c daalein aur ye x = (−b ± √(b² − 4ac)) / 2a apply karta hai, discriminant dikhata hai jo root ka type decide karta hai aur parabola y = ax² + bx + c ka vertex bhi. Jab discriminant negative hota hai, calculator error dikhane ke bajaye conjugate pair ko a+bi aur a−bi format mein dikhata hai. Ye algebra students ke liye hai jo homework check kar rahe hain, teachers ke liye jo worked examples banate hain, aur kisi bhi aise insaan ke liye jise physics ya engineering problem mein fast, reliable second root chahiye. Sab kuch aapke browser mein locally chalta hai — jo coefficients aap type karte hain wo kabhi aapke device se bahar nahi jaate.

Features

ax² + bx + c = 0 ko ek hi step mein dono roots ke liye solve karta hai
Real, repeated, aur complex conjugate roots automatically handle karta hai
Discriminant b² − 4ac dikhata hai taaki aap dekh sakein roots aise kyu aaye
Complex roots ko clearly a+bi aur a−bi format mein dikhata hai
Graphing ke liye parabola ka vertex (x, y) calculate karta hai
Equation aur results ka plain-text summary copy karta hai
a = 0 ko clear message ke saath reject karta hai, silent galat answer nahi deta
Poori tarah aapke browser mein chalta hai, equation ka data kahin bhi bheja nahi jaata

Quadratic Formula Calculator kaise use karein

x² term ka coefficient a daalein
x term ka coefficient b daalein
constant c daalein
discriminant, dono roots, aur vertex padhein, ya summary copy karein

Example

Input

x²-3x+2=0

Output

x = 2, x = 1

a=1, b=-3, c=2 (x-2)(x-1) ki tarah factor hota hai, isliye roots 2 aur 1 hain.

Common errors aur troubleshooting

a = 0 daalne par root ke bajaye error aata hai. — Jab a 0 hota hai to equation linear ban jaati hai, quadratic nahi — Quadratic Formula Calculator ise flag karta hai kyunki formula apply karne ke liye koi ax² term hi nahi hai.
Result mein numbers ke bajaye 1+2i aur 1−2i jaise roots dikhte hain. — Iska matlab discriminant negative hai, isliye equation ke real solutions nahi hain — 1+2i aur 1−2i sahi complex conjugate roots hain.
Equation ko '3x2-5x+2' bina operators ke type karne se fields confuse ho jaate hain. — Calculator har box mein ek coefficient expect karta hai (a, b, c) — poori equation text ki tarah likhne ke bajaye 3, -5, aur 2 alag-alag daalein.
Negative b ya c ignore ho jaata hai. — Minus sign field mein hi include karein, jaise b ke liye alag se subtraction karne ke bajaye -3 type karein — calculator sign ko number ka hi part maanta hai.

Aksar pooche jaane wale sawaal

Quadratic Formula Calculator kya solve karta hai?: Ye ax² + bx + c = 0 form ki koi bhi equation solve karta hai, x = (−b ± √(b² − 4ac)) / 2a use karke x ke dono values deta hai, saath hi discriminant aur parabola ka vertex bhi.
Discriminant kya hota hai aur ye kyun important hai?: Discriminant b² − 4ac hota hai. Positive value ka matlab do alag real roots, zero ka matlab ek repeated real root, aur negative value ka matlab dono roots complex conjugate hain.
Complex roots ka format kaisa hota hai?: Jab discriminant negative hota hai, Quadratic Formula Calculator pair ko a+bi aur a−bi likhta hai, aur agar real part zero ho aur imaginary coefficient 1 ho to sirf i ya −i tak simplify kar deta hai.
Calculator a = 0 ko kyun reject karta hai?: Agar a 0 hai to x² term hi khatam ho jaata hai aur equation linear (bx + c = 0) ban jaati hai, jo quadratic nahi hai — calculator zero se divide karne ke bajaye error dikhata hai.
Roots ke saath dikhaya gaya vertex value kya hai?: Ye parabola y = ax² + bx + c ka vertex (x, y) hai, jo x = −b / 2a par calculate hota hai. Ye parabola ka minimum ya maximum point hota hai, graph banane mein useful.
Kya is calculator ka use karte waqt meri equation kahin bhejii jaati hai?: Nahi. Quadratic Formula Calculator har result aapke browser mein hi calculate karta hai — jo coefficients aap daalte hain wo kabhi ArrayKit par upload nahi hote.

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