Roots of a quadratic equation 3x²-x+9=0 are p and q. Value from p/q + q/p = ... ?

Hello,

3x²-x+9=0

==>x²-x/3+3=0

p+q=1/3

pq=3

p/q+q/p=[ (p+q) ²-2pq] / (pq) = [ (1/3) ²-2*3]/3=[1/9-6]/3=-53/27

3x² - x + 9 = 0

also x² - (1/3) x + 3 = 0

p, q are roots so

(x - p) (x - q) = x² - (1/3) x + 3 = 0

x² - (p+q) x + pq = x² - (1/3) x + 3 = 0

compare coefficients we have

p+q = 1/3 ... (1)

pq = 3 ... (2)

(1) / (2) ... (p+q) / pq = (1/3) / 3

p/q + q/p = 1/9