Mathematics · Class 10
Polynomials
Relationship between zeroes and coefficients; division algorithm for polynomials.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Class 10 Polynomials links zeroes and coefficients of quadratic polynomials, division algorithm, and graph behaviour. This chapter connects algebra to coordinate geometry.
Zeroes and Coefficients
For ax² + bx + c
Sum of zeroes α + β = −b/a
Product of zeroes
αβ = c/a
Division algorithm
p(x) = g(x)q(x) + r(x), deg r < deg g
Graphical Meaning
- Zeroes are x-intercepts of y = p(x)
- At most n zeroes for degree n polynomial
- Parabola opens up if a > 0, down if a < 0
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Sum and product
Find sum and product of zeroes of 2x² − 8x + 6.
- 1a = 2, b = −8, c = 6
- 2Sum = −b/a = 8/2 = 4
- 3Product = c/a = 6/2 = 3
Answer
Sum = 4, Product = 3
Example 2: Form polynomial
Form quadratic with zeroes 2 and −3.
- 1x − 2 and x + 3 are factors
- 2p(x) = k(x − 2)(x + 3)
- 3= k(x² + x − 6); take k = 1
Answer
x² + x − 6
Key Points to Remember
- ✓ If α, β are zeroes, polynomial is k[x² − (α+β)x + αβ]
- ✓ Remainder on division by (x − a) is p(a)
- ✓ Cubic has at most 3 zeroes
Exam Tips
- • Verify zeroes by substitution
- • Use sum/product relations for missing zero
- • State degree of remainder in division
Practice MCQs — Polynomials
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Sum of zeroes of x² − 5x + 6 is: