Are these statements true or false and why?

a) Not all quadratic function have zeros.


b) every cubic function has at least 1 zero


c) Not all cubic functions have zeros


d) every quartic function has at least 1 zero





I have a test tomorrow and i'm clueless about this so if anyone could help it would be greatly appreciated. Thank you.Are these statements true or false and why?
a) true. x^2 + 3 is above the x axis and will never intercept it, thus it has no zeros


b) True. The cubic function extends from either negative to positive infinity or vice versa, There is always one side of it that will flow below the x- axis, being an odd function as well (exponents are odd numbers)


c) False. Proven above...i hope


c) False. due to letter a. Both quartic and quadratic are even, thus they resemble parabolas. And simply shifted them upwards will clear them from the x-axis. Are these statements true or false and why?
I dont know