Search problems

2 problems match “rational equations”. Clear

Visitors search a sample. Sign in for free to search every problem. Sign in

1. Complex solutions of a rational equation ●●○○○ 20 ptsFind the number of complex solutions to $\frac{z^3 - 1}{z^2 + z - 2} = 0$.
2. Candle burn-out time from catch-up times ●●●○○ 50 ptsThree candles have the same length but different thicknesses, and each burns at a constant rate until it burns out completely. The first candle was lit 1 hour earlier than the other two, which were lit at the same time. At some moment the first and third candles had the same length, and 2 hours after that moment the first and second candles had the same length. The second candle burns out in 12 hours and the third in 8 hours. How many hours does it take for the first candle to burn out?