Question

If c is a real number and if 2+i is a solution of the equation x^2-4x+c, what is the value of c

Answer 1

2nd degree with real coefients
so if a+bi is a root then a-bi is also a root
if 2+i is a root then 2-i is also a root

so, the factored form of a quadratic equation with roots r1 and r2 is
(x-r1)(x-r2)

so
2+i and 2-i

(x-(2+i))(x-(2-i))
(x-2-i)(x-2+i)
expanding we get
x²-4x+5
so c=5