Quadratic equations

Let the required quadratic equation be x^2-px+q=0

Sum of two roots:
p=(5+i)/3+(5-i)/3=(5+i+5-i)/3=10/3

Product of roots:
q=[(5+i)/3][(5-i)/3]=(5+i)(5-i)/9=(25+1)/9=26/9

Therefore the required quadratic equation is:
x^2-10x/3+26/9=0
9x^2-30x+26=0

i think the quadratic equation is better to expressed in the simplest form,and the coefficients and the constant term of the equation should all be intergers,i.e. 9x^2-30x+26=0

9x^2-30x+26=0
18x^2-60x+52=0
27x^2-90x+78=0
4.5x^2-15x+13=0
36x^2-120x+104=0
45x^2-150x+130=0
3x^2-10x+26/3=0
90x^2-300x+260=0
... ...