Question

If f(x) is a polynomial with real coefficients and zeros of 4(multiplicity 2 ), -1(multiplicity2 ),-1+8i , and 2-2i, what is the minimum degree of f(x) ?

Answer 1

The minimum degree of polynomial f(x) = 6

Explanation:

Multiplicity for a polynomial equation is the number of times the polynomial has that particular root.

The roots of this polynomial is given as

4(multiplicity 2 ), -1(multiplicity2 ), (-1+8i), and (2-2i)

Hence, the true roots of this particular polynomial are 4, 4, -1, -1, (-1+8i), and (2-2i)

Making a total of 6 roots.

The number of roots of a polynomial is the minimum degree of such a polynomial.

Hence, the minimum degree of this polynomial is 6.

Hope this Helps!!!