(a)

The polynomial function .

Find the real zeros of the function by equating to zero.

.

Thus, the real zeros are .

(b)

The degree of polynomial function " f " has " n " real zeros and the graph of " f " has, at most " " turning points.

The polynomial function .

The degree of polynomial function is 2.

Thus, the graph has  turning point.

\ \

The factor , k > 1, yields a repeated zero x = a of multiplicity k.

If k is odd, the graph crosses the x - axis at x = a.

The polynomial function .

The factor form of polynomial function .

Since the factor has k = 1, the multiplicity is odd.

(c)

The polynomial function .

1. Draw the coordinate plane.

2. Graph the function .

Graph : \ \

(a)

The real zeros are .

(b)

Odd multiplicity.

One turning point.

(c)

Graph of the function is :