Let u and v be the solutions to \(3x^2 + 5x + 7 = 0\) Find \(\frac{u}{v} + \frac{v}{u}\)

By the quadratic formula, the roots are -1/6*i*sqrt(59) - 5/6 and i/6*i*sqrt(59) + 5/6. Then

u/v + v/u = (1/6*i*sqrt(59) - 5/6)/(i/6*i*sqrt(59) + 5/6) + (1/6*i*sqrt(59) - 5/6)/(i/6*i*sqrt(59) + 5/6)

u/v + v/u = 3/4

Right idea (almost!) but you have the wrong signs

\(u=\frac{-5+i\sqrt{59}}{6}\\v = \frac{-5-i\sqrt{59}}{6}\)

I'm sorry, but that's incorrect

I assume, from this comment, that you know what the answer is ?

If that's the case, why are you asking the question ?

My teacher graded it as incorrect, so I'm not sure why. She wants corrections.