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

Feb 5, 2021

#1
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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

Feb 5, 2021
#5
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Right idea (almost!) but you have the wrong signs

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

Alan  Feb 5, 2021
edited by Alan  Feb 5, 2021
#2
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I'm sorry, but that's incorrect

Feb 5, 2021
#3
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I assume, from this comment, that you know what the answer is ?

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

Guest Feb 5, 2021
#4
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My teacher graded it as incorrect, so I'm not sure why. She wants corrections.

Guest Feb 5, 2021