To get to work sam jogs 3 kilometers to the train, then rides the remaining 5 kilometers. if the train goes 40 km per hour faster than sam’s constant rate of jogging and the entire trip takes 30 minutes, how fast does sam jog?

Let
r = Sam's jogging rate
r+40 = train's rate

The rate refers to a speed of any moving body.
Know first the relationship of distance, time, and rate. The time is the distance divided by the rate.
By analyzing the problem, the time for Sam and the time for train have the total time of 30 minutes or 1/2 hours. Expressing it into an equation yields
t(Sam) + t(train) = 1/2 hours
The distance covered by Sam is 3 km, and the distance covered by train is 5 km. So
3/s + 5/(s+40) = 1/2
Solving for s,
3(s+40) + 5s = (1/2)*(s(s+40))
3s + 120 + 5s = (1/2)s² + 20s
8s + 120 = (1/2)s² + 20s
(1/2)s² + 12s - 120 = 0

The solution is turned out into a quadratic equation. If you know the quadratic formula, you get for x, for instance the two values of x are
s = 7.59 and s = -31.59

The value s = -31.59 is meaningless. Therefore Sam's jogging rate is 7.59 km/hr.

Answer to your question: a. the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. the roots are ​ x=1±i7√2 .number of roots=degree of polynomialhere, degree of polynomial is 2 so number of roots will be 2.hope it *_*