Find a polynomial equation with real coefficients that has the given zeros.

Question

1-7i and 1+7i

the equation consists of x^2- (?)x+(?)=0

thanks for your help

Answer 1

Set up Roots: (x - (1 - 7i)(x - (1+7i) = 0

Foil x² - x(1 + 7i) - x(1 - 7i) + (1-7i)(1+7i) = 0

Simplify: x² - x - x7i - x + x7i + (1 + 7i - 7i - 49i²) (i² = -1)

Simplify: x² - 2x + 1 + 49

answer: x² - 2x + 50