Form a polynomial f(x) with real coefficients

Question

Degree:5 Zeroes: 7; - i; 7+i

Answer 1

Hello Jackie

In case you have not already answered this question, here is the solution.

First of all, two zeros are missing, i.e., i and 7 - i. So the factors are: (x - 7)(x - i)(x + i)[x - (7 + i)][x - (7 - i)] =

(x - 7)(x² + 1)[x² - x(7 - i) - x(7 + i) + 49 + 1] = (x - 7)(x² + 1)(x² - 7x + xi - 7x -xi + 50) =

(x³ - 7x² + x - 7)(x² - 14x + 50) = x⁵ - 14x⁴ + 50x³ - 7x⁴ + 98x³ - 350x² + x³ - 14x² + 50x - 7x² + 98x - 350

= x⁵ - 21x⁴ + 149x³ - 371x² + 148x - 350.

Sincerely

Michael I.