Question

Write a polynomial of least degree with real coefficients and with the root
–5+13𝑖

Answer 1

the other root is -5-13i, so
y = (x-(-5+3i))(x-(-5-13i))
y = ((x+5)-13i)((x+5)+13i)
y = (x+5)^2 + 13^2
y = x^2+10x+194

Answer 2

or
sum of roots = -5-13i + -5+13i = -10
product of roots = (-5-13i)(-5+13i)
= 25 - 169i^2 = 25+169 = 194

x^2 + 10x + 194

Answer 3

I like it!