Sunday, February 1, 2009

solving a fourth degree equation given one of its complex roots

solve 2x^4-8x^3+19x^2-22x+5=0 given that 1+2i is one of its roots

complex roots occur in conjugate pairs if the coefficients are real
so 1-2i is also a root
{x - (1+2i)}{x - (1-2i)} is a factor
multiply into a quadratic
divide the given equation by this quadratic factor to extract the other quadratic factor and solve that

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