# 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.

**Q2: **

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

**Q3: **

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

- A cannot say
- B no
- C yes

**Q4: **

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

**Q5: **

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

- A no
- B yes

**Q6: **

How many roots does the polynomial have?

**Q7: **

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

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

**Q8: **

Are the roots of the equation real and different?

- Ano
- Byes

**Q9: **

Given that has a zero at and , determine the values of , , and .

- A , ,
- B , ,
- C , ,
- D , ,
- E , ,

**Q10: **

If 7 and 6 are the roots of the equation , what are the values of and ?

- A ,
- B ,
- C ,
- D ,
- E ,

**Q11: **

If the roots of the equation have a difference of 3, what is the value of ?

**Q12: **

Find the quadratic equation whose roots are and .

- A
- B
- C
- D

**Q13: **

How many real solutions does the equation have?

**Q14: **

Determine the type of the roots of the equation , if and are real numbers.

- Areal
- Bcomplex and not real

**Q15: **

Let be a complex cube root of unity. Form a quadratic equation whose roots are and .

- A
- B
- C
- D
- E

**Q16: **

Determine the type of the roots of the equation .

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

**Q17: **

Determine the type of the roots of the equation .

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

**Q18: **

Determine the quadratic equation whose roots are and .

- A
- B
- C
- D

**Q19: **

Find the quadratic equation whose two roots are and .

- A
- B
- C
- D