Answer
(a) 4 real zeros.
(b) 2 real and 2 non-real zeros.
(c) 4 non-real zeros.
Work Step by Step
(a) We graph the function as shown in the figure (a). Clearly there are 4 intersection points between the function and the x-axis, indicating 4 real zeros in this case.
(b) See graph (b), there are two intersection points between the function and the x-axis, hence, there are 2 real zeros. As it is a 4th order polynomial, there must be 2 non-real zeros as required by the Zeros theorem.
(c) See graph (c), the minimum of the function is at $(1.366,39.75)$ and there are no intersection points
between the function and the x-axis, indicating that there are no real zeros. According to the Zeros Theorem,
there must be 4 non-real zeros.