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some imp. pts abt quadratic equations..... 1) Remember the foll. points while solving a quadratic equation.. a) x2 + y2 = (x+y)2 - 2xy b) x3 + y3 = (x+y)3 - 3xy(x+y) c) x4 + y4 = (x2+y2)2 - 2x2y2 d) x5 + y5 = (x2 + y2)(x3 + y3) - x2y2(x+y) e) x - y = ( (x+y)2 - 4xy)1/2 2) If ax2 + bx + c is satisfied by more than 2 values , its an identity and a = b = c = 0 3)Common roots -> if ax2 + bx + c = 0 & px2 + qx + r = 0 have a common root(@) , then @2/br - qc = @/pc - ar = 1/aq - bp eliminating @ , we get (pc - ar)2 = (br - qc)(aq - pb).. b)T
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submitted by chimanshu_007 (11504 m) on 11 Aug 2007 02:52:04 IST (14 comments 789 views)
