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for following 1) 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?...

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1) 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: The least is 3 roots (6 complex, one real). On the other hand, all roots could be distinct, so at most 7 distinct roots.

(2 complex roots and 5 real roots, 4 complex roots and 3 real roots or 6 complex roots and 1 real root)


2) What are the zeroes of f(x) = x^3 + 5x^2 -7x + 1?

answer: x=1, -3 +-√10


3) X^8-1 is divided by x-2, the remainder would be?

answer:255

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