Class 10 Maths - GUJARAT
Polynomials
The chapter Polynomials in Class 10 Mathematics under the Gujarat Secondary and Higher Secondary Education Board (GSEB) introduces students to the foundational algebraic expressions that build the base for higher-level math. You will learn about the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of linear and quadratic polynomials, and the division algorithm for polynomials. This chapter is extremely scoring in board exams, frequently featuring short-answer questions and a 2 to 3-mark analytical problem based on finding a quadratic polynomial when its sum and product of zeroes are given.
Start Learning FreeKey Concepts
Degree of a Polynomial
The highest power of the variable in a polynomial is called its degree, which determines the maximum number of zeroes the polynomial can have.
Geometrical Meaning of Zeroes
The zeroes of a polynomial 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 ax² + bx + c, the sum of zeroes equals -b/a and the product of zeroes equals c/a.
Division Algorithm for Polynomials
It states that if p(x) and g(x) are two polynomials where g(x) ≠ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x).
Important Formulas
Board Exam Info
In the Gujarat (GSEB) Class 10 Mathematics board exam, this chapter typically carries around 4 to 6 marks. Common question types include finding the zeroes of a given quadratic polynomial, verifying the relationship between zeroes and coefficients, forming a quadratic polynomial from given sum and product of zeroes, and performing polynomial division.
Frequently Asked Questions
What is the difference between a polynomial and an algebraic expression?
All polynomials are algebraic expressions, but not all algebraic expressions are polynomials. Polynomials cannot have variables with negative or fractional exponents, and variables cannot be in the denominator.
How do I find a quadratic polynomial if the sum and product of its zeroes are given?
You can directly use the formula: p(x) = k[x² - (sum)x + (product)], where k is a non-zero real constant.
Why is the remainder zero sometimes in the division algorithm?
When the remainder r(x) is zero, it means the divisor g(x) is an exact factor of the dividend p(x).
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