165x Filetype PPT File size 2.32 MB Source: www.ssgopalganj.in
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non- negative, whole- number exponents. Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences; they are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. Let x be a variable n, be a positive integer and as, a ,a ,….a be constants 1 2 n (real nos.) Then, f(x) = a xn+ a xn-1+….+a x+x n n-1 1 o a xn,a xn-1,….a x and a are known as n n-1 1 o the terms of the polynomial. a ,a ,a ,….a and a are their n n-1 n-2 1 o coefficient s. For example: • p(x) = 3x – 2 is a polynomial in variable x. • q(x) = 3y2 – 2y + 4 is a polynomial in variable y. • f(u) = 1/2u3 – 3u2 + 2u – 4 is a polynomial in variable u. •A polynomial of degree 1 is called a Linear Polynomial. Its general form is ax+b where a is not equal to 0 •A polynomial of degree 2 is called a Quadratic Polynomial. Its general form is ax3+bx2+cx, where a is not equal to zero •A polynomial of degree 3 is called a Cubic Polynomial. Its general form is ax3+bx2+cx+d, where a is not equal to zero. •A polynomial of degree zero is called a Constant Polynomial LINEAR POLYNOMIAL For example: p(x) = 4x – 3, q(x) = 3y are linear polynomials. Any linear polynomial is in the form ax + b, where a, b are real nos. and a ≠ 0. QUADRATIC POLYNOMIAL For example: 2 2 f(x) = √3x – 4/3x + ½, q(w) = 2/3w + 4 are quadratic polynomials with real coefficients.
no reviews yet
Please Login to review.