Class 10 Maths NCERT Exemplar: Quadratic Equations

Important Solved Question for CBSE Board

Yeh page ek important NCERT Exemplar question aur uska detailed solution provide karta hai, jo Class 10 Maths ke chapter 'Quadratic Equations' se liya gaya hai. Isse students apne concepts clear kar sakte hain aur board exam ki taiyari acche se kar sakte hain.

Question Topic: Nature of Roots

Is question mein hum quadratic equation ke roots ki nature (real, equal, imaginary) find karenge.

Here we have provided NCERT Exemplar Questionfor Class 10 Maths in hindi Language, Just select the chapters below to get Exemplar Solution of the same:

वास्तविक संख्याएँ

बहुपद

दो चरों में रैखिक समीकरण युग्म

द्विघात समीकरण

समान्तर श्रेढ़ी

त्रिभुज

निर्देशांक ज्यामिति

त्रिकोणमिति का परिचय और उसके अनुप्रयोग

वृत्त

रचनायें

वृत्त से सम्बंधित क्षेत्रफल

पृष्ठीय क्षेत्रफल और आयतन

सांख्यिकी और प्रायिकता

उत्तरमाला

NCERT Exemplar Question on Quadratic Equations

Yeh question Class 10 Maths NCERT Exemplar book Chapter 4 'Quadratic Equations' se liya gaya hai. Yeh question board exams mein frequently pucha jata hai aur iska concept bahut important hai.

Original Question from NCERT Exemplar

Question: Find the nature of the roots of the following quadratic equation. If the real roots exist, find them: 2x² - 6x + 3 = 0

Step-by-Step Solution in Hinglish

Chalo is question ko step-by-step solve karte hain:

Step 1: Identify Coefficients

Hamare paas quadratic equation hai: 2x² - 6x + 3 = 0
Standard form ax² + bx + c = 0 ke according:
a = 2, b = -6, c = 3

Step 2: Find Discriminant (D)

Discriminant formula hai: D = b² - 4ac
D = (-6)² - 4 × 2 × 3
D = 36 - 24
D = 12

Step 3: Determine Nature of Roots

Kyunki D > 0 (D positive hai), isliye:
• Roots real aur distinct honge
• Roots unequal honge
• Roots do honge

Step 4: Calculate Roots Using Quadratic Formula

Quadratic formula hai: x = [-b ± √D] / 2a
x = [6 ± √12] / (2 × 2)
x = [6 ± 2√3] / 4
x = [3 ± √3] / 2

Isliye, roots hain:
x₁ = (3 + √3) / 2
x₂ = (3 - √3) / 2

Step 5: Final Answer

Nature of roots: Real and distinct
Real roots: (3 + √3)/2 and (3 - √3)/2

Why This Question is Important for CBSE Board Exam

1. Direct formula application: Yeh question discriminant aur quadratic formula dono ka use karna sikhata hai.
2. Concept clarity: Nature of roots ka concept clear ho jata hai.
3. Board exam pattern: Aise questions frequently board exams mein aate hain.
4. Step marking: Step-by-step solution se full marks milte hain.

Common Mistakes Students Make

• Sign mistake: b = -6 hai, iska square karte time sign ka dhyaan rakhna.
• Calculation error: 4ac calculate karte time 4 × 2 × 3 = 24, isme galti na karen.
• Simplification: √12 = 2√3 simplify karna na bhoolen.
• Final answer: Roots ko simplest form mein likhna zaroori hai.

Practice Questions for Self-Assessment

1. Find nature of roots: 3x² - 4√3x + 4 = 0
2. Find roots if real: x² + 7x + 10 = 0
3. Check if roots are equal: 2x² - 3x + 5 = 0

Key Formulas to Remember

• Discriminant: D = b² - 4ac
• Nature of roots: D > 0 (real, distinct), D = 0 (real, equal), D < 0 (no real roots)
• Quadratic formula: x = [-b ± √D] / 2a
• Standard form: ax² + bx + c = 0, where a ≠ 0

CBSE Marking Scheme for Such Questions

Agar aap board exam mein aisa question solve karte hain to marks is tarah milte hain:
• Correct formula application: 1 mark
• Correct discriminant calculation: 1 mark
• Correct nature determination: 1 mark
• Correct roots calculation: 1 mark
• Final answer: 1 mark

Total: 5 marks ka question. Isliye har step sahi likhna zaroori hai.

Tips for Solving Quadratic Equations Questions

1. Always write given equation clearly.
2. Identify coefficients a, b, c correctly.
3. Calculate discriminant carefully without sign mistakes.
4. Determine nature based on D value.
5. Use quadratic formula only if D ≥ 0.
6. Simplify the final answer properly.
7. Always check your solution by putting values back in original equation.

Yeh NCERT Exemplar question practice karke aap Quadratic Equations chapter mein confident ho jaoge. Board exam mein aise questions regularly aate hain, isliye iska solution acche se samajh lena chahiye.