SOLUTION: If a 4th degree equation, with integral coeffecients, has roots 2-i, and 1+√(3), find the equation for the polynomial.
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Question 699319: If a 4th degree equation, with integral coeffecients, has roots 2-i, and 1+√(3), find the equation for the polynomial.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Both complex zeros and irrational zeros always appear in conjugate pairs. Hence, if 
is a zero, then 
is also a zero. If 
is a zero, then 
is also a zero.
If 
is a zero of a polynomial equation, then 
must be a factor of the polynomial.
Hence:
)(x\ -\ (2\ +\ i))(x\ -\ (1\ +\ \sqrt{3}))(x\ -\ (1\ -\ \sqrt{3})))
is the fully factored polynomial. Multiply out the factors and set the resulting 4th degree polynomial equal to zero. Hint: Multiply the first two binomial factors then the last two binomial factors. Treat the inner parentheticals as a single term. Remember that the product of a pair of real number conjugates is the difference of two squares, and the product of a pair of complex conjugates is the sum of two squares.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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