college algebra...?

Question

*form a quadratic equation whose roots are 1/2(2+i) and 1/2(2-i)
*determine the nature of the roots of the quadratic equation 4x2+12x+9=0
*find the solution set: x/x+1 +5/8 = 5/2(x+1) + 2/4
*word problem: a jet plane traveling at a rate of 550 mph overtakes another plane that had a 3 hour head start and is travelling at a rate of 250 mph. how far from the starting point does the jet overtake the other plane?
*give the function of least possible degree whose roots are 1+2i, 1-2i, 2+-square root of 5, -3
*solve the linear system by Cramer's rule: x+3y=7 , y+z=5 , 2x-4z= -10
*word problem: a cyclist traveled a certain distance at her usual speed. if her speed had been 2mi/hr faster, she would have traveled the ditance in 1hr less time. if her speed had been 2mi/hr slower, she would have taken 2hrr longer. find the distance traveled and her ususal speed.

-p.s can anyone solve this..? PLEASE!

Answer 1

word problem - cyclyst
hmmmmm - almost have it solved - except
is it (IF 2 mph slower - cyclist would have taken twice as long) instead of 2 hrs longer??
time x rate = distance
(time -1) x (rate +2)
(2 time) x (rate-2)
time= 3 and rate = 4
3 x 4 = 12
2 x 6 = 12
and
6 x 2 = 12 but that's if twice as much time versus 2 hrs longer

all the best

Answer 2

1)x^2-2x+5/4=0

2) There is one real root.

4) (x-1-2i)(x-1+2i)(x-2+sqrt5)(x+3)=0