If the function ax^5+ bx^3+c has five roots which of a, b and c cannot be zero?

For a function f(x) which has five roots, the highest
power of x should be 5. We are given f(x) = ax^5 + bx^3 +
c.

So this has to have the highest power of x as 5,
therefore 'a' cannot be zero else the expression will have a highest power of
3.

Also c cannot be zero, because if it is taken to be
zero, the expression is reduced to ax^5 + bx^3= x^3(ax^2+b), this can have a maximum of
three roots including 0.

If b is zero the expression is
ax^5+c. Now equating ax^5+c=0,

x^5 = c/a . Now this also
cannot yield 5 values of x.

So neither of  a , b or c can
be zero if the expression has 5 roots.