A root of equation ax 2 +bx+c=0 (Where a,b and c rational numbers

| A root of equation ax2+bx+c=0 (Where a,b and c rational numbers) is 5+3√3. What is the value of (a2+b2+c2)/(a+b+c)?

A. 35/3

B. 37/3

C. -105/11

D. -105/13

SOLUTION

If one root is 5+3√3 which is irrational, then the other root has to be 5-3√3.
Since a, b and c are rational numbers.
ax2+bx+c = (x–5-3√3)(x-5+3√3)
=
=
After comparing
a=1, b=-10, c=-2
(a2+b2+c2)/(a+b+c)
= (1+100+4)/(1-10-2)
= -105/11