solving a fourth degree equation with real coefficients if you are given one of the imaginary roots

solving a fourth degree equation with real coefficients if you are given one of the imaginary roots

solve x^4 - 4 x^3  + 11 x^2  -14x +10 =0  given that  1+2i   is  one of the roots.

since the coefficients of the given equation are real, the complex roots will occur in conjugate pairs

so 1-2i is another root.

using this you can find a quadratic factor of the given fourth degree expression.

use long division or comparision of coeffecients to extract the other quadratic factor and solve it

some questions in mathematics for the tamilnadu higher secondary 12th exam, isc ,  puc pre degree etc.
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