Quadratic Equation Solver

Quadratic Equation Solver Quadratic Equation Solver – User may choose the constants a, b & c for the quadratic equation to be solved. Applet will show the graph and the roots of the equation along with suitable comment. User may try different combinations of a, b & c and see the graph. This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com General form of Quadratic equation is ax^2 + bx + c = 0. Values of x satisfying the Quadratic equation are known as roots. Graphical of Geometrical method to get roots: Plot the function y = ax^2 + bx + c. Cutting points of this quadratic equation are known as zeros of the function. x coordinates of the cutting points (or zeros) are known as the roots of the equation. The plot may cut x axis at two, one or none of the points i.e. the plot may be wholly up or down of the x axis. Following cases arise. Case 1: The graph cuts x axis at P(x1,0) & Q(x2,0) then quadratic equation has two real roots R1 = x1 & R2 = x2. Case 2: The graph cuts x axis at one point P(x1,0) then quadratic equation has two real roots which have same value i.e. R1 = R2 = x1. Case 3: The doesn't cut x axis. The quadratic equation has no real roots. It has imaginary roots. There are found by algebra. Algebraic Solution: Here the roots are R1, R2 = [ -b ± √(b2 - 4ac)]/(2a) Expression under root sign D = (b2 - 4ac) decides the nature of roots and hence is known as discriminant. Following special cases arise: Case 1: D = 0, R1 = R2 = - b/(2a) two roots are identical. X2 - 2x + 1 D = 0 R1 = R2 = 1 Case 2: D is +ve b = 0 R1 = √D & R2 = - √D Case 3: D is – ve Roots are complex as √D is imaginary Then R1 = (-b + √D I)/(2a) and R2 = (-b - √D I)/(2a) There are further sub-cases with different combinations of zero & nonzero values of a, b & c. Dr Barve, 30 August 2014, Created with GeoGebra