Well here's my attempt at the first one.
$We have the polynomial $ p(x)=x^2 + bx + c $, where $ c $ and $ b $ are real.$
$Let the roots be $ \alpha, \beta $ such that $ |\alpha| < 1 $ and $ |\beta|<1.
$From sum and products of roots, it follow that $ \alpha + \beta = -b $ and $ \alpha...
As stated above, 1eV = 1.6 x 10^-19 J
eV stands for electronvolt, it's just another unit of energy, but it is related to an electron. You could use joules, it doesn't matter.
It's not hard, it is fun though, was probably my favourite topic in MX2! When you first look at it, it looks hard, but when you do it it's not really :p
When the car is going down the hill, the forces acting upon it are
F=mg(\frac{1}{30}) - kv_d^2 \\ $The car is travelling at a constant velocity, and so $ F=0 \\ mg(\frac{1}{30}) = kv_d^2 \\ k = \frac{mg(\frac{1}{30})}{v_d^2}
Now that we know k, we have everything we need to find the force...