# Worksheet: Real and Complex Roots of Polynomials

In this worksheet, we will practice finding the number and type of roots of polynomials and finding unknown coefficients if the roots are given.

**Q1: **

If is a root of the polynomial , what is the value of ?

**Q2: **

Does the polynomial , where is nonzero and all the coefficients are real, have at least one real root?

- A no
- B cannot say
- C yes

**Q3: **

If is a root of the equation , where is a polynomial with real coefficients, which other complex number must also be a root?

- A
- B
- C
- D
- E

**Q4: **

Is it possible for a polynomial with real coefficients to have exactly 3 non-real roots?

- A yes
- B no

**Q5: **

How many roots does the polynomial have?

**Q6: **

How many real roots could the polynomial have given that , and are all real?

- A 4 or 2
- B 5, 3, or 1
- C only 2
- D only 1
- E4, 2, or 1

**Q7: **

Determine the type of the roots of the equation .

- Areal and different
- Bcomplex and not real
- Creal and equal

**Q8: **

Determine the type of the roots of the equation .

- Acomplex and not real
- Breal and equal
- Creal and different

**Q9: **

Solve the equation , .

- A
- B
- C
- D

**Q10: **

Given that is one of the roots of the equation , find the other two roots.

- A
- B
- C
- D

**Q11: **

Find the solution set of in the set of complex numbers.

- A
- B
- C
- D
- E