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

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