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

| A root of equation ax

^{2}+bx+c=0 (Where a,b and c rational numbers) is 5+3√3. What is the value of (a^{2}+b^{2}+c^{2})/(a+b+c)?A. 35/3

B. 37/3

C. -105/11

D. -105/13

Please scroll down to ** see the correct answer ** and ** solution guide.**

### Right Answer is: C

#### 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.

ax^{2}+bx+c = (x–5-3√3)(x-5+3√3)

=

=

After comparing

a=1, b=-10, c=-2

(a^{2}+b^{2}+c^{2})/(a+b+c)

= (1+100+4)/(1-10-2)

= -105/11