Answer
(a) $x=-\sqrt 3$ (multiplicity 2) and $x=2$ (multiplicity 4).
(b) $x=-\sqrt 3$ and $x=2$ touches the x-axis.
(c) $5$.
(d) $y=x^6$.
Work Step by Step
(a) For $f(x)=(x+\sqrt 3)^2(x-2)^4$, we can list real zero as $x=-\sqrt 3$ (multiplicity 2) and $x=2$ (multiplicity 4).
(b) At $x=-\sqrt 3$ and $x=2$ the graph touches the x-axis.
(c) The maximum number of turning points on the graph is given by $n-1=6-1=5$.
(d) As $n=6, a_6\gt0$, the end behaviors are rise to the right and rise to the left, similar to $y=x^6$.