Solution of Equations || Chapter 1 || Engineering Mathematics in English
52 videos • 311 views • by Manas Patnaik The expression 𝒇(𝒙)=𝒂_𝒐 𝒙^𝒏+𝒂_𝟏 𝒙^(𝒏−𝟏)+ 𝒂_𝟐 𝒙^(𝒏−𝟐)……… 𝒂_(𝒏−𝟏) 𝒙+ 𝒂_𝒏, where a's are constants (cannot equal to 0) and n is a positive integer, is called a Polynomial in x of degree n. The polynomial f(x) = 0 is called an algebraic equation of degree n. If (x) contains some other functions such as trigonometric, logarithmic, exponential etc. ; then f(x) = 0 is called a transcendental equation. The value of x which satisfies f(x) = O, is called its root. Geometrically, a root of (1) is that value of x where the graph of y = f(x) crosses the x-axis. The process of finding the roots of an equation is known as the solution of that equation. This is a problem of basic importance in applied mathematics. We often come across problems in deflection of beams, electrical circuits and mechanical vibrations which depend upon the solution of equations. As such, a brief account of solution of equations are given in this chapter. 1. Introduction 2. General Properties 3. Transformation of Equations 4. Reciprocal Equations 5. Solutions of Cubic Equations by Cardan's Method 6. Solution of Bi-quadratic Equations by Ferrari's Method 7. Graphical Solution of Equations #engineeringmathematics #solutionofequation #gate