1. Solve each equation, then state the number and type
of roots.
one real root
two real roots

2. one real root and two imaginary roots

3. two real roots and two imaginary roots

4. Write a polynomial function of least degree with
integer coefficients whose zeros include 2, 1 and -3
x=2 x=1 x = -3
x–2=0 x–1=0 x+3=0
(x – 2)(x – 1)(x + 3) = 0
(x2 – 3x + 2)(x + 3) = 0
x3 + 3x2 – 3x2 – 9x + 2x + 6 = 0
x3 – 7x + 6 = 0

5. Write a polynomial function of least degree with
integer coefficients whose zeros include 4 and 4 – i.
Complex
x=4 x=4–i x=4+i zeros occur
in
x–4=0 x–4+i=0 x–4–i=0 conjugate
pairs
(x – 4) (x – 4 + i) (x – 4 – i) 
    +1
x2 – 4x – xi – 4x + 16 + 4i + xi – 4i – i2
(x – 4) x2 – 8x + 17

6. Pg. 372

7. State the possible number of positive real zeros, negative
real zeros, and imaginary zeros of
2 sign changes
+  + +
2 or 0 positive zeros
f(-x) = (-x)3 – (-x)2 + 2(-x) + 4
1 sign change
=  x3 – x2 – 2x + 4 1 negative zero
   +
2 or 0 imaginary zeros.

8. State the possible number of positive real
zeros, negative real zeros, and imaginary zeros of
2 sign changes
+  + + +
2 or 0 positive zeros
p(-x) = (-x)4 – (-x)3 + (-x)2 + (-x) + 3
2 sign changes
= x4 + x3 + x2 - x + 3
2 or 0 negative zeros
+ + +  +
4, 2, or 0 imaginary zeros.