# Worksheet: Solving Quadratic Equation with Complex Roots

In this worksheet, we will practice solving quadratic equations whose roots are complex numbers.

**Q2: **

Which of the following best describes the roots of the equation ?

- Atwo complex roots
- Btwo non-real roots
- Cone repeated real root
- Done repeated non-real root

**Q3: **

Solve the equation .

- A
- B
- C
- D
- E

**Q4: **

Given that is one of the roots of , determine the value of .

- A
- B
- C
- D

**Q5: **

Find the roots of the quadratic equation .

- A
- B
- C
- D
- E

**Q7: **

Find the solution set of .

- A
- B
- C
- D

**Q9: **

Find the solution set of over .

- A
- B
- C
- D

**Q10: **

If the discriminant of a quadratic equation with real coefficients is negative, will its roots be a complex conjugate pair?

- AYes
- BNo

**Q11: **

Factor over the complex numbers.

- A
- B
- C
- D
- E

**Q12: **

Solve the equation .

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

**Q13: **

Which quadratic equation has roots ?

- A
- B
- C
- D
- E

**Q14: **

Solve the quadratic equation .

- A
- B
- C
- D
- E

**Q15: **

Solve the quadratic equation .

- A
- B
- C
- D
- E

**Q16: **

Solve the quadratic equation .

- A
- B
- C
- D
- E

**Q17: **

Find the value of such that the quadratic equation has the roots .

**Q18: **

By completing the square, solve the equation .

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

**Q19: **

The product of the roots of the equation is 4. Find the value of and the solution set of the equation.

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

**Q20: **

Factor over the complex numbers.

- A
- B
- C
- D
- E

**Q21: **

The complex numbers and , where , , , and are real numbers, are roots of a quadratic polynomial with real coefficients. Given that , what conditions, if any, must , , , and satisfy?

- Athere are no additional conditions
- B and
- C and
- D and

**Q23: **

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

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

**Q24: **

Given that is one of the roots of the equation , find the other root and the value of .

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

**Q25: **

Find all possible values of , where , for which .

- A6, 2
- B6, 2, ,
- C ,
- D6, 2, ,
- E ,