Class 10 Maths (Ganit) Chapter 2 PDF: बहुपद (Polynomials)

Class 10 Maths Chapter 2, Polynomials, connects the geometrical meaning of the zeroes of a polynomial (x-intercepts of $y = p(x)$) with the algebraic relationship between the zeroes and coefficients of quadratic and cubic polynomials.

What Class 10 Mathematics (Ganit — Hindi Medium) Chapter 2 Covers

2.1 & 2.2 Geometrical Meaning of the Zeroes of a Polynomial shows that the zeroes of a polynomial $p(x)$ are precisely the x-coordinates of the points where the graph of $y = p(x)$ intersects the x-axis: a linear polynomial $ax + b$ (a ≠ 0) is a straight line with one zero ($-b/a$), and a quadratic polynomial ax² + bx + c (a ≠ 0) is a parabola opening upwards ($a > 0$) or downwards ($a < 0$) with at most 2 real zeroes.

2.3 Relationship between Zeroes and Coefficients of a Polynomial shows that if α and β are the zeroes of p(x) = ax² + bx + c, then α + β = -b/a and αβ = c/a, and conversely a quadratic polynomial with given sum S and product P of zeroes is k(x² – Sx + P); it also states the sum, pairwise product and product formulas for a cubic polynomial ax³ + bx² + cx + d.

Exercises in Chapter 2

• Exercise 2.1 (1 Question, 6 graphs) finds the number of zeroes of $p(x)$ by counting the points where the graph of $y = p(x)$ intersects or touches the x-axis.
• Exercise 2.2 (2 Questions, 12 parts) finds the zeroes of quadratic polynomials by splitting the middle term, verifies α + β = -b/a and αβ = c/a, and constructs quadratic polynomials from given sums and products of zeroes.

Read Class 10 Mathematics (Ganit — Hindi Medium) Chapter 2 Online

More Chapters

• Previous: Chapter 1: वास्तविक संख्याएँ (Real Numbers)
• Next: Chapter 3: दो चर वाले रैखिक समीकरण युग्म (Pair of Linear Equations in Two Variables)
• English medium: Class 10 Maths Chapter 2 PDF in English
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FAQ

What is the relationship between the zeroes and coefficients of a quadratic polynomial?
If α and β are the zeroes of the quadratic polynomial p(x) = ax² + bx + c (a ≠ 0), then the sum of zeroes is α + β = -b/a and the product of zeroes is αβ = c/a.

How many zeroes can a polynomial of degree n have?
A polynomial of degree n can have at most n real zeroes—its graph $y = p(x)$ intersects the x-axis at most n times.