Class 10 Maths Chapter 2: Polynomials Concept Infographic (NCERT)

← Back to Class List

✦ NCF 2023 ALIGNED • VISUAL LEARNING SERIES ✦

Chapter 2: Polynomials

Decoding Degrees, Graphing Zeroes, and Coefficient Relationships[cite: 3].

📘 Degree 1: Linear

Form: ax + b (a ≠ 0)

Highest power of x is 1[cite: 3].
Examples: 2x - 3, √3x + 5[cite: 3].

Zero Calculation:
If p(k) = 0, then ak + b = 0 ⇒ k = -b/a[cite: 3].

📗 Degree 2: Quadratic

Form: ax² + bx + c (a ≠ 0)

Highest power of x is 2. The word comes from 'quadrate' meaning 'square'[cite: 3].
Example: 2x² + 3x - 5[cite: 3].

Max Zeroes: 2 (Can have 2 distinct, 2 equal, or 0 zeroes)[cite: 3].

📙 Degree 3: Cubic

Form: ax³ + bx² + cx + d (a ≠ 0)

Highest power of x is 3[cite: 3].
Example: 3x³ - 2x² + x - 1[cite: 3].

Max Zeroes: 3[cite: 3].

📈 Geometrical Meaning of Zeroes

The zeroes of p(x) are precisely the x-coordinates of the points where the graph of y = p(x) intersects the x-axis[cite: 3].

Linear Graph

Straight line. Intersects exactly ONCE at (-b/a, 0)[cite: 3].

Quadratic Graph

Parabola (U-shape)[cite: 3]. Intersects at MOST twice[cite: 3].

🔗 Zeroes & Coefficients Relation

For quadratic polynomial ax² + bx + c, with zeroes α and β[cite: 3]:

Sum: α + β = -b / a[cite: 3]

=  -

Coefficient of x Coefficient of x²

Product: αβ = c / a[cite: 3]

=  

Constant term Coefficient of x²

⭐ Board Exam Super-Hacks

Building Polynomial from Zeroes

If you are given the sum (S) and product (P) of zeroes, the quadratic polynomial can be quickly formed using:
k[x² - (Sum)x + (Product)][cite: 3] or k(x² - Sx + P).

Graph Intersection Rule

A polynomial p(x) of degree n can intersect the x-axis at at most n points[cite: 3]. Therefore, it has at most n zeroes[cite: 3]. Count the x-axis touches to find the number of zeroes!

⚠️ Common Exam Traps

Trap 1: The Missing Minus Sign

When calculating the Sum of zeroes (α + β = -b/a), students often forget the negative sign[cite: 3]. Always write the formula first to avoid missing it.

Trap 2: Recognizing Polynomials

Expressions with negative powers (e.g., 1/x - 1) or fractional powers (e.g., √x + 2) are NOT polynomials[cite: 3]. Ensure all powers of x are whole numbers.

Designed by Akash Srivastva | Mathematics Hub • Visual Learning Series

🚀 Loved this? Get more visual study materials at: www.akashmaths.online