For the 2025–2026 academic year, the most important topics in Class 10 Maths for the chapter on Polynomials revolve around
the zeroes of polynomials and their relationship with the coefficients, particularly for quadratic polynomials. The division algorithm for polynomials has been removed.
Key topics in polynomials
- Geometrical meaning of zeroes: You must understand how the number of zeroes of a polynomial relates to the number of times its graph intersects the x-axis. Expect to analyze and interpret graphs of linear, quadratic, and cubic polynomials to determine their number of zeroes.
- Relationship between zeroes and coefficients: This is a crucial area for problem-solving, focusing specifically on quadratic polynomials.
- Finding zeroes: You should be able to find the zeroes of a given quadratic polynomial by factorization.
- Verifying the relationship: Once the zeroes (
αalpha𝛼 and βbeta𝛽) are found, you must verify the relationship with the coefficients (aa𝑎, bb𝑏, and cc𝑐) using the following formulas:- Sum of zeroes: α+β=−baalpha plus beta equals negative b over a end-fraction𝛼+𝛽=−𝑏𝑎
- Product of zeroes: αβ=caalpha beta equals c over a end-fraction𝛼𝛽=𝑐𝑎
- Sum of zeroes:
- Constructing a polynomial: You should be able to construct a quadratic polynomial when the sum and product of its zeroes are given.
- Important question types: Practice questions that require you to find the value of a coefficient (like k or p) when a zero of the polynomial is given or when a specific relationship exists between the zeroes.
Deleted topic for 2025–2026
- Division Algorithm for Polynomials: The statement and simple problems based on the division algorithm for polynomials with real coefficients are no longer part of the CBSE syllabus. Problems involving the division of a polynomial by another polynomial will not be assessed.
