Polynomials is Chapter 2 of CBSE Class 10 Maths (NCERT). In CBSE Board 2024, this chapter contributed 6–8 marks. Understanding zeroes, relationship between zeroes and coefficients, and the Division Algorithm is essential for full marks.
Types of Polynomials
| Type | Degree | Max Zeroes | Example |
|---|---|---|---|
| Constant | 0 | 0 | p(x) = 5 |
| Linear | 1 | 1 | p(x) = 2x + 3 |
| Quadratic | 2 | 2 | p(x) = x² − 5x + 6 |
| Cubic | 3 | 3 | p(x) = x³ − 3x + 2 |
Zeroes of Polynomial
A zero of p(x) is a value ‘a’ where p(a) = 0. Geometrically: x-coordinates where graph touches/crosses x-axis.
Example: p(x) = x² − 5x + 6 = (x−2)(x−3) → zeroes are 2 and 3
Relationship Between Zeroes and Coefficients
Quadratic ax² + bx + c (zeroes: α, β)
| Relationship | Formula |
|---|---|
| Sum: α + β | −b/a |
| Product: αβ | c/a |
Cubic ax³ + bx² + cx + d (zeroes: α, β, γ)
| Relationship | Formula |
|---|---|
| Sum: α+β+γ | −b/a |
| Sum of products (two at a time): αβ+βγ+γα | c/a |
| Product: αβγ | −d/a |
Division Algorithm
p(x) = g(x) × q(x) + r(x)
Dividend = Divisor × Quotient + Remainder
Condition: degree(r) < degree(g), OR r = 0
Key Results to Remember
- One zero = reciprocal of other → product = 1 → c/a = 1 → c = a
- One zero = negative of other → sum = 0 → b = 0
- Both equal → discriminant = 0 → b² = 4ac
- p(x) = x² + 1 has NO real zeroes (graph never touches x-axis)
Forming Quadratic Polynomial
Given zeroes α and β: p(x) = k[x² − (α+β)x + αβ]
Example: Zeroes 3 and −4 → Sum = −1, Product = −12 → p(x) = x² + x − 12
Practice MCQs — Polynomials (CBSE Class 10)
Practice Quiz — 10 CLAT-Style Questions
Click an option to reveal the answer and explanation.
Last updated: April 2026 | Ready For Boards — Expert CBSE Class 10 preparation
