Question 289436
Let the roots be x & y
xy=1/4
x+y=3/2
x=3/2 -y
y(3/2 -y)=1/4
3y/2 - y^2 = 1/4
6y-4y^2=1
4y^2-6y+1=0
y=(3-sqrt(5)), y=(3+sqrt(5)) or vice versa. 
y-(3-sqrt(5))* y-(3+sqrt(5))
=y^2-6y+4
.
Ed