Question

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed.
5 ​(multiplicity 2), 7+i​ (multiplicity 1)

Answer 1

Required polynomial = (x - 5)^2 (x - 7 - i))(x - 7 + i)) = (x^2 - 10x + 25)(x^2 - 7x + ix - 7x + 49 - 7i - ix + 7i + 1) = (x^2 - 10x + 25)(x^2 - 14x + 50) = x^4 - 24x^3 + 215x^2 - 850x + 1250