Question

1. Complete the square to form a perfect square trinomial. 8x + x² + __

A. 16
B. 4
C. 8
D. 2

2. Solve the equation by completing the square. x² + 4x = 12
A. 3, -4
B. -6, 2
C. 4, -4
D. -4, 3

3. Find the number of real solutions using the discriminant. x² + 9x + 4 = 0
A. 0
B. 1
C. 2

4. Find the number of real solutions using the discriminant. x² - 6x - 7 = 0
A. 2
B. 1
C. 0

Answer 1

1. x² + 8x + 16
x² + 4x + 4x + 16
x(x) + x(4) + 4(x) + 4(4)
x(x + 4) + 4(x + 4)
(x + 4)(x + 4)
(x + 4)²
The answer is A.

2. x² + 4x = 12
x² + 4x + 4 = 12 + 4
x² + 4x + 4 = 16
x² + 2x + 2x + 4 = 16
x(x) + x(2) + 2(x) + 2(2) = 16
x(x + 2) + 2(x + 2) = 16
(x + 2)(x + 2) = 16
(x + 2)² = 16
√(x + 2)² = √16
x + 2 = ±4
- 2 - 2
x = -2 ± 4
x = -2 + 4 or x = -2 - 4
x = 2 or x = -6
The answer is B.

3. x² + 9x + 4 = 0
Δ = b² - 4ac
Δ = (9)² - 4(1)(4)
Δ = 81 - 4(4)
Δ = 81 - 16
Δ = 65
THe answer is C.

4. x² - 6x - 7 = 0
Δ = b² - 4ac
Δ = (-6)² - 4(1)(-7)
Δ = 36 - 4(-7)
Δ = 36 + 28
Δ = 64
The answer is A.