# Worksheet: Solving Quadratic Equation with Complex Roots

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

Q1:

Determine the solution set of over the set of complex numbers.

• A
• B
• C
• D

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

Q6:

Solve the equation over the set of complex numbers.

• A
• B
• C
• D4
• E

Q7:

Find the solution set of .

• A
• B
• C
• D

Q8:

Find the solution set of given .

• 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:

• A
• B
• C
• D
• E

Q15:

• A
• B
• C
• D
• E

Q16:

• 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

Q22:

Determine the type of the roots of the equation .

• Areal and different
• Breal and equal
• Ccomplex and not real

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,