# Lesson Worksheet: Real and Complex Roots of Polynomials Mathematics

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?

- ANo
- BYes
- CThe answer cannot be determined.

**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 nonreal roots?

- ANo
- BYes

**Q5: **

How many roots does the polynomial have?

**Q6: **

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

- Aonly 2
- B5, 3, or 1
- Conly 1
- D4 or 2
- E4, 2, or 1

**Q7: **

Determine the type of the roots of the equation .

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

**Q8: **

Determine the type of the roots of the equation .

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

**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