I. INTRODUCTORY PROBLEMS

1. (i) What is the condition for the quadratic polynomial to have (a) no real root, (b) two real zeros ?

(ii) How many real zeros have the polynomials:

(a) (b) (c)

(d)

where they exist, find the root(s).

(iii) Find the real zeros of the following polynomials:

(a) (b) (c)

2. (i) Show that , and hence state the number of real zeros of the polynomial .

(ii) Determine the real zeros of the polynomials

(a) (b) (c)

3. Determine the zeros of the polynomials P(*x*) and hence sketch the curve y = P(*x*)

(a) (b)

(c) (d)

(e) (f)

4. Sketch the following curves:

(a) (b)

hence determine the set of values of *x* for which the polynomials

(i) < 0 (ii) __>__ 0

5. Find the real zeros of the following polynomials P(*x*) and hence sketch the curve:

(a) (b) (c)

(d) (e) (f)