Chapter 4: Quadratic Equations – Class 10 CBSE Maths Notes with Formulas & Examples
๐ฉ Class 10 Maths Chapter 4 – Quadratic Equations | CBSE Notes with Examples
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This article provides complete, exam-focused notes for Class 10 CBSE Maths Chapter 4 – Quadratic Equations. If you’re a Class 10 student preparing for your board exam, this chapter is very important. Let’s dive into definitions, methods, formulas, and solved examples.
๐ท What is a Quadratic Equation?
A quadratic equation is any equation of the form:
ax² + bx + c = 0, where a ≠ 0.
Examples:
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2x² + 3x – 5 = 0
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x² – 4x + 4 = 0
Here, a, b, c are real numbers, and x is the variable.
๐น Standard Form and Key Terms:
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Quadratic Term: ax²
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Linear Term: bx
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Constant Term: c
Example:
In the equation 3x² – 7x + 2 = 0,
a = 3, b = –7, c = 2
๐ถ Methods to Solve a Quadratic Equation
Class 10 CBSE syllabus teaches three main methods:
1. Factorization Method
Split the middle term and factor the equation.
Example:
x² – 7x + 12 = 0
= x² – 3x – 4x + 12 = 0
= x(x – 3) – 4(x – 3) = (x – 4)(x – 3) = 0
So, x = 3 or 4
2. Completing the Square Method
Make LHS a perfect square.
Example:
x² + 6x + 5 = 0
⇒ x² + 6x = –5
⇒ x² + 6x + 9 = –5 + 9
⇒ (x + 3)² = 4
⇒ x + 3 = ±2
⇒ x = –3 ± 2 ⇒ x = –1 or –5
3. Quadratic Formula
Use the formula:
x = [–b ± √(b² – 4ac)] / 2a
Example: Solve 2x² + 3x – 5 = 0
a = 2, b = 3, c = –5
Discriminant (D) = b² – 4ac = 9 + 40 = 49
x = [–3 ± √49] / 4 = [–3 ± 7]/4
x = 1 or –2.5
๐ท Nature of Roots (Based on Discriminant)
Let D = b² – 4ac
| Discriminant D | Nature of Roots |
|---|---|
| D > 0 | Two distinct real roots |
| D = 0 | Two equal real roots |
| D < 0 | No real roots (imaginary) |
๐ Class 10 CBSE Exam Tips
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Use the quadratic formula when factorization is tough.
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Always check discriminant to know the type of roots.
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Revise standard identities like (a ± b)², etc.
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Practice NCERT exercises and exemplar problems.
✅ Sample Board Question
Q. Solve the quadratic equation: 3x² – x – 4 = 0
a = 3, b = –1, c = –4
D = (–1)² – 4×3×(–4) = 1 + 48 = 49
x = [1 ± √49]/6 = [1 ± 7]/6
x = 8/6 = 4/3 or x = –1
Answer: x = 4/3 or –1
๐ Summary
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Quadratic Equations are essential for scoring well.
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Three solving methods: factorization, completing square, quadratic formula
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Discriminant helps determine root nature
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Practice is key for speed and accuracy
๐ Read Other Chapters – Class 10 CBSE Maths Notes
-
๐ Chapter 5: Arithmetic Progressions – Coming Soon
๐ฅ Download Chapter 4 Notes PDF
You can download the full PDF for Chapter 4 – Quadratic Equations from the link below:
๐ Download Chapter 4 PDF on Instamojo
๐ Explore More Chapters
๐ Click here to download all Class 10 CBSE Maths chapters – Real Numbers, Polynomials, Linear Equations, and more.
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