2011/060)If a^2=5a-3, b^2=5b-3, then equation having a/b and b/a as its roots is___?

a is not equal to b
A. 3x^2+19x+3
B. 3x^2-19x+3
C. 3x^2-19x-3
D. x^2-16x+1
Ans:
since a^2=5a-3, b^2=5b-3
a,b are soln's for the eqn. x^2=5x-3
ie x^2-5x+3=0
and they are not same so they are 2 roots of x^2-5x+3=0

hence sum of roots =a+b= -(-5/1) =5
and product of roots=ab=+( 3/1)=3

now if a/b and b/a are roots then

sum of the roots is
a/b + b/a = a^2 + b^2 /ab =(a+b)^2 -2ab /ab =5^2 -2*3 /3 =25-6 /3=19/3

and product is a/b *b/a =1

so eqn wth roots a/b&*b/a is
x^2 -(19/3)x +1 =0
=>3x^2-19x+3=0

hence the ans is B