Polynomials
NCERT Solutions for Class 10 Maths Chapter 1- Real Numbers
Polynomials are a mathematical expression that consists of variables, coefficients, and exponents. It is an algebraic expression with one or more terms, where each term is a product of a coefficient and one or more variables raised to non-negative integer exponents.
The general form of a polynomial is:
P(x) = a_n * x^n + a_{n-1} * x^{n-1} + … + a_1 * x + a_0
where P(x) is the polynomial, x is the variable, a_n, a_{n-1}, …, a_1, a_0 are the coefficients, and n is a non-negative integer representing the degree of the polynomial.
Polynomials are named based on their degrees. The degree of a polynomial is determined by the highest exponent of the variable in the expression. For example, a polynomial with a degree of 3 is called a cubic polynomial, while a polynomial with a degree of 2 is called a quadratic polynomial.
Polynomials are fundamental in algebra and have various applications in mathematics, physics, engineering, and other fields. They can be used to represent and solve equations, model real-world problems, approximate functions, and analyze mathematical properties.
Polynomials have important properties, such as the ability to be added, subtracted, multiplied, and divided. Polynomial division allows us to find quotients and remainders when dividing one polynomial by another, which can be useful for various mathematical operations and problem-solving.
In summary, polynomials are algebraic expressions that play a central role in mathematics. They are versatile tools for modeling, analyzing, and solving a wide range of mathematical problems in different disciplines.
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NCERT Class 10 Maths Chapter 2
Exercise 2.1
1. The graphs of y = p(x) are given in Fig. 2.10 below, for some polynomials p(x). Find the number of zeroes of p(x), in each case.
(i) The graph of p(x) is parallel to the x-axis and does not intersect it at any point. Therefore, the number of zeroes of p(x) is 0.
(ii) The graph of p(x) intersects the x-axis at one point. Therefore, the number of zeroes of p(x) is 1.
(iii) The graph of p(x) intersects the x-axis at three distinct points. Therefore, the number of zeroes of p(x) is 3.
(iv) The graph of p(x) intersects the x-axis at two points. Therefore, the number of zeroes of p(x) is 2.
(v) The graph of p(x) intersects the x-axis at four distinct points. Therefore, the number of zeroes of p(x) is 4.
(vi) The graph of p(x) intersects the x-axis at three points. Therefore, the number of zeroes of p(x) is 3.