tag:blogger.com,1999:blog-4546875473573140085.post2241205956676737301..comments2011-11-08T15:02:07.513+08:00Comments on SST Class Blog S108 (Yr 2010): HW reminder for 11/10/10 (By Eunice)Mr James Koh http://www.blogger.com/profile/05961292618303617628noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-4546875473573140085.post-74200334061343422602011-11-08T15:02:07.513+08:002011-11-08T15:02:07.513+08:00Quadratic Equation is a polynomial equation of sec...Quadratic Equation is a polynomial equation of second degree. The general form of a quadratic equations is ax2+bx+c = 0.<br /><br />The contributions of the ancient Indian Mathematicians to quadratic equations are quite significant and extensive. Before 800BC Indian Mathematicians constructed 'altars' based on the solutions of quadratic equation ax2+bx+c =0, Aryabhatta gave a rule to sum the geometric series which involves the solution of a quadratic equation.<br /><br /><br /><br />Discriminant of Quadratic EquationBack to Top<br />The following table shows the nature of the roots of a quadratic equation with rational coefficients.<br /><br />Discriminant 2 Square root<br />= 0 perfect rational and equal<br />> 0 <br />perfect or not perfect<br /><br />rational and unequal (or) <br /><br />irrational and unequal roots<br /><br />< 0 not perfect complex and conjugate roots in pair<br />Formation of a Quadratic EquationBack to Top<br />Let us form the quadratic equation whose roots are and .<br /><br />Then x = , y = are the roots<br /><br />Therefore x - = 0 and<br /><br />, y -<br /><br />so (x - ) (y - <br /><br />Maximum and Minimum Values of a Quadratic ExpressionBack to Top<br />An expression of the type ax2+bx+c is called " quadratic expression".<br /><br />The quadratic expression ax2+bx+c takes different values as x takes different values.<br /><br />As x varies from - to + ax2+bx+c<br /><br />has a minimum value whenever a> 0.<br />The minimum value of the quadratic expression is (4ac-b2 )/4a and it occurs at x = - b/2a.<br /><br />2. has a maximum value whenever a< 0.<br /><br />The maximum value of the quadratic expression is (4ac-b2 )/4a and it occurs at x = - b/2a.<br /><br />Quadratic Equation FormulaBack to Top<br />The general form of a quadratic equations is ax2+bx+c = 0 .<br /><br />The set of all solutions of a quadratic equation is called its solution set. The values of x that make a quadratic equation true is called its roots or zeros or solutions. Quadratic equations can be solved by factorization method or by using quadratic formula<br /><br />x = (-b± √(b²-4ac))/(2a)<br /><br />quadratic formula<br /><br />[x = (-b+-sqrt(b] 2 [-4ac))/(2a)]<br /><br />[where b] 2 [ -4ac] [ is called the discriminant of the quadratic equation.] [ A quadratic equation has two roots. ]<br /><br />I have given only explanation of Algebaric expression .So you can visit here for broadway :-<br />so visit <a href="http://logarithmsrulesandformula.wordpress.com/2011/10/21/how-to-solve-logarithm-problems/" rel="nofollow">algebraic expressions</a>Akithttp://www.blogger.com/profile/01683966784216474351noreply@blogger.com