Class 10 Maths - KARNATAKA
Polynomials
In the Class 10 Mathematics chapter on Polynomials, Karnataka SSLC students explore the geometrical meaning of zeroes of a polynomial and the relationship between zeroes and coefficients. You will learn about linear, quadratic, and cubic polynomials, and practice division algorithms for polynomials. This chapter forms the foundation of algebra and appears consistently in board exams through 1-mark objective questions, 2-mark short answers, and 3-mark graph-based problems. Mastering this chapter ensures you can easily score full marks in the algebraic sections of your SSLC mathematics question paper.
Start Learning FreeKey Concepts
Degree of a Polynomial
The highest power of the variable in a polynomial is called its degree. For example, the degree of 3x^2 + 5x - 2 is 2, making it a quadratic polynomial.
Zeroes of a Polynomial
The values of the variable for which the value of the polynomial becomes zero are called its zeroes. Geometrically, they are the x-coordinates of the points where the graph of the polynomial intersects the x-axis.
Relationship between Zeroes and Coefficients
For a quadratic polynomial ax^2 + bx + c, the sum of zeroes is equal to -b/a and the product of zeroes is equal to c/a.
Division Algorithm for Polynomials
If p(x) and g(x) are any two polynomials with g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).
Important Formulas
Board Exam Info
In the Karnataka SSLC (KSEEB) Mathematics board exam, Polynomials typically carries around 4 to 6 marks. Common question types include finding the zeroes of a quadratic polynomial and verifying the relationship with coefficients, forming a quadratic polynomial when the sum and product of zeroes are given, and solving division algorithm problems.
Frequently Asked Questions
How do I find the zeroes of a quadratic polynomial?
You can find zeroes by factorizing the middle term (splitting the middle term) so that the polynomial is expressed as a product of two linear factors, and then equating each factor to zero.
What does the graph of a quadratic polynomial look like?
The graph of a quadratic polynomial ax^2 + bx + c is a parabola. It opens upwards if a > 0 and downwards if a < 0.
Is the division algorithm compulsory for SSLC board exams?
Yes, problems based on the division algorithm and checking whether a polynomial is a factor of another are frequently asked in 2 or 3-mark questions.
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