Quadratic equation (द्विघात समीकरण) | Concept + Practice | Maths by nigam sir

Описание: Quadratic equation (द्विघात समीकरण) | Concept + Practice | Maths by nigam sir

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🔷 Quadratic Equation (द्विघात समीकरण) – Extra Long Description
Quadratic Equation ek aisa algebraic equation hota hai jisme variable (अचर) ka highest power 2 hota hai. Agar kisi equation me variable ka square term (x²) present ho, to us equation ko Quadratic Equation kaha jata hai.
📌 Standard Form (मानक रूप)
Quadratic equation ka standard form hota hai:
jahaan –
a ≠ 0
a, b, c real numbers hote hain
x variable hota hai
📌 Yahan a quadratic term ka coefficient, b linear term ka coefficient aur c constant term hota hai.
🔷 Quadratic Equation ke Example
�
�
�
Yeh sab quadratic equations hain kyunki inme variable ka highest power 2 hai.
🔷 Quadratic Equation ko Solve karne ke Methods
Quadratic equation ko solve karne ke 3 main methods hote hain:
1️⃣ Factorization Method (गुणनखंड विधि)
Is method me equation ko factors me todkar roots nikale jaate hain.
Ye method tab easy hota hai jab factors easily mil jaate ho.
2️⃣ Completing the Square Method (पूर्ण वर्ग विधि)
Is method me equation ko is tarah se modify kiya jata hai ki perfect square ban jaaye.
Ye method theoretical understanding ke liye bahut important hota hai.
3️⃣ Quadratic Formula Method (सूत्र विधि)
Sabse universal method, jo har quadratic equation par apply hota hai.
Is formula se hum directly equation ke roots nikal sakte hain.
🔷 Discriminant (D) ka Concept
Quadratic equation me Discriminant bahut important role play karta hai.
Discriminant ki value se roots ki nature pata chalti hai:
D 0 → Do alag-alag real roots
D = 0 → Do equal real roots
D 0 → Koi real root nahi (imaginary roots)
📌 Competitive exams me discriminant se related questions bahut aate hain.
🔷 Roots of Quadratic Equation (द्विघात समीकरण के मूल)
Quadratic equation ke 2 roots hote hain, jo equation ko satisfy karte hain.
Roots ka sum aur product bhi important hota hai:
Sum of roots = �
Product of roots = �
In formulas ka use karke bina poori equation solve kiye bhi kaafi questions easily solve ho jaate hain.
🔷 Graphical Interpretation
Quadratic equation ka graph Parabola hota hai.
Agar a 0 → Parabola upar ki taraf open hota hai
Agar a 0 → Parabola neeche ki taraf open hota hai
Graph ke x-axis ko jahan parabola cut karta hai, wahi quadratic equation ke roots hote hain.
🔷 Exams me Importance
Quadratic equation ka topic bahut important hai:
UPTET / CTET
SSC (CGL, CHSL, MTS)
UP SI, Police, Banking
Board Exams
Is topic se direct questions, MCQs, aur application based problems aate hain.
🔷 Conclusion (निष्कर्ष)
Quadratic equation mathematics ka ek fundamental topic hai, jo algebra ke kai advanced topics ka base banata hai. Agar students is topic ke concepts, methods aur discriminant ko achhe se samajh lein, to wo exams me bina confusion ke questions solve kar sakte hain.
👉 Practice + Concept clarity = Quadratic Equation mastery 💯