Which of the following represents the complex solution(s) to the quadratic equation, 0 = 2x² + 4?

1. x = - √2


2. x = √-2i


3. x = i √2


4. x = ±2i

A
Incorrect. This does not represent a complex number. This is simply a negative irrational number.

B
Incorrect. The number i will not appear inside a radical.

C
Correct! Isolate x² then take the square root of both sides.

D
Incorrect. These are solutions to y = x^2 + 4.

The quadratic equation y = x² − 2x + 6 has no real solutions. Which of the following are correct solution(s) to this equation?

1. 1 + 2i√5 and 1 − 2i√5
2. 1 + i√20 and 1 − i√20
3. 2 + i√5 2 and 2 − i√5 2
4. 1 + i√5 and 1 − i√5

A
Incorrect. Check your work, there was a mistake when you simplified.

B
Incorrect. Check your work, there was a mistake when you simplified.

C
Incorrect. Missing a factor in the numerator.

D
Correct! The quadratic formula was used to find the solution to the equation.

1. x = -3 ± 2i√2
2. x = -3 ±i√2
3. x = -6 ±i√11
4. x = -6 ± 2i√11

A
Incorrect. The 2 in 2i divides out when simplified.

B
Correct! The quadratic formula was used and simplified correctly.

C
Incorrect. Incorrect number under the radical in the quadratic formula.

D
Incorrect. Incorrect number under the radical in the quadratic formula.

The complex conjugates 2 ± 3i√7 could be complex solutions to which of the following equations?

1. x²- 4x − 59 = 0
2. x²- 4x + 67 = 0
3. x²- 4x − 63 = 0
4. x²+ 4x + 59 = 0

A
Incorrect. This one will have real solutions.

B
Correct! First check the discriminant, it is negative, use the quadratic equation to see if this is the equation for the solution given.

C
Incorrect. This one will have real solutions.

D
Incorrect. b² − 4ac = 16 − 236 = -200