Polynomial Function

Question

  Write a polynomial function of least degree with integral coefficients that has the given zeros.   

2i, 1+ squareroot2

Answer 1

f(x) = (x - 2i)(x + 2i)[x - (1+√2)][x - (1 - √2)]

= (x² + 4)[(x - 1) - √2][(x - 1) + √2]

= (x² + 4)[(x - 1)² - 2]

= (x² + 4)(x² - 2x - 1) = x⁴ - 2x³ - x² + 4x² - 8x - 4 = x⁴ - 2x³ + 3x² - 8x - 4