Question 885523: . What are the least, and most, amount of distinct zeroes of a 7th degree polynomial, given that at least one root is a complex number?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if the equation is 7th degree then it has 7 roots.
those roots can be complex or real.
complex roots always come in pairs, so if it has one, then it has 2, the other one being the conjugate of the first one.
in other words, if one complex root is a + bi, then the other complex root is a - bi.
if at least one root is complex, then you would have a minimum of 2 complex roots with a maximum of 5 real roots.
the equation can have at most 6 complex roots (3 pairs) so the minimum number of real roots is equal to 1.
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