If you want scoring marks in board exam, start with JKBOSE Class 10th Maths Polynomials Notes. This is Chapter 2 of JKBOSE 10th Maths, and questions from zeroes and their relationship with coefficients appear almost every year.
When I prepared for my Class 10 board exam, I revised this chapter one night before Maths paper. One question came directly from relationship between zeroes and coefficients.
Quick Summary – JKBOSE 10th Maths Chapter 2
| Topic | Details |
|---|---|
| Chapter | Polynomials (Chapter 2) |
| Class | 10th JKBOSE |
| Main Focus | Zeroes of Polynomial, Relationship with Coefficients |
| Common Marks Area | 1, 2 and 3 mark questions |
| Level | Easy and Formula Based |
What is a Polynomial
A polynomial is an expression made of variables and constants combined using addition, subtraction and multiplication.
Example: 3x² + 5x − 2
In Polynomials Class 10 JKBOSE, you mainly study quadratic polynomials.
Types of Polynomials
Based on Degree
- Linear Polynomial: Degree 1 (Example: 2x + 3)
- Quadratic Polynomial: Degree 2 (Example: x² + 5x + 6)
- Cubic Polynomial: Degree 3 (Example: x³ + 2x² + x)
Degree means highest power of variable.
Zeroes of a Polynomial
A zero of a polynomial is the value of x that makes the polynomial equal to 0.
Example: If p(x) = x² − 4
Put p(x) = 0 → x² − 4 = 0 → x = 2 or −2
So 2 and −2 are zeroes.
Relationship Between Zeroes and Coefficients
This is the most important part of JKBOSE Class 10th Maths Polynomials Notes.
For quadratic polynomial:
ax² + bx + c
| Formula | Meaning |
|---|---|
| Sum of zeroes = −b/a | α + β |
| Product of zeroes = c/a | αβ |
If you remember these two formulas, you can solve most board questions.
Example: Find sum and product of zeroes of 2x² + 7x + 3
a = 2, b = 7, c = 3
Sum = −b/a = −7/2
Product = c/a = 3/2
In exam, always write formula first. Then substitute values.
Division Algorithm for Polynomials
If p(x) and g(x) are two polynomials and g(x) ≠ 0, then:
p(x) = g(x) × q(x) + r(x)
This is similar to Euclid Division Lemma from Chapter 1.
Remainder degree must be less than divisor degree.
Long division method is used in exam.
Graphical Meaning of Zeroes
Zeroes of a polynomial are the points where its graph cuts the x-axis.
- Linear polynomial → cuts once → one zero
- Quadratic polynomial → cuts twice → two zeroes
- If graph does not cut x-axis → no real zero
Graph-based question is short and direct.
Key Formulas – Polynomials
| Formula | Use |
|---|---|
| α + β = −b/a | Sum of zeroes |
| αβ = c/a | Product of zeroes |
| p(x) = g(x)q(x) + r(x) | Division Algorithm |
Important Questions for JKBOSE Exam
1. Find zeroes of x² − 5x + 6.
2. Find sum and product of zeroes of 3x² − 7x + 2.
3. Verify relationship between zeroes and coefficients.
4. Divide 2x³ + 3x² − x + 5 by x + 2.
5. Find number of zeroes from given graph.
Relationship question comes almost every year in JKBOSE 10th Maths Chapter 2.
Exam Tips from Dar Zaid
- Focus area: Sum and product formula. It is direct scoring.
- Common mistake: Students forget minus sign in −b/a. Always check sign before writing answer.
- Division method: Write neatly in column form. Do not mix steps.
- Time tip: Attempt Polynomials after Real Numbers. Both are formula based and quick.
For full syllabus coverage, visit JKBOSE Class 10th Maths Notes – Chapter Wise.
Frequently Asked Questions
How many marks does Polynomials carry in JKBOSE?
Usually 3 to 5 marks come from Polynomials in JKBOSE Class 10 Maths paper.
What is the relationship between zeroes and coefficients?
For ax² + bx + c, the sum of zeroes is −b/a and the product of zeroes is c/a.
Is Polynomials important for JKBOSE Class 10?
Yes. It is Chapter 2 and formula based. You can score full marks with proper practice.
What is Division Algorithm for Polynomials?
It states that p(x) = g(x)q(x) + r(x), where the degree of r(x) is less than the degree of g(x).
How to find zeroes of a quadratic polynomial?
Factorize the expression and set it equal to 0. Then solve for x to find the zeroes.
