Unformatted text preview: a 3 If '4 + 27 > 0, there will be one real root and two conjugate complex roots; 6 2 a J If 4' + 27 0, there will be three real roots of which at least two are equal: b 2 a J If "4 + 27 < 0, there will be three real and unequal roots. o There are other methods to find roots. The NewtonRalphson iterative formula uses the first derivative and normally converges nicely in just a few iterations. Excel, Quattro, and Lotus have builtin "solver" functions. MathCAD software will do this easily (probably overkill). Many scientific calculators also have builtin "solver" functions. o After obtaining an answer, the wise engineer plugs it back into the original equations to verify the solution....
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 Fall '08
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 Quadratic equation, Elementary algebra, cubic equation, conjugate complex roots, CRC Math Handbook

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