Answer:
(4 x + 9) (16 x^2 - 36 x + 81)
Step-by-step explanation:
Factor the following:
64 x^3 + 729
64 x^3 + 729 = (4 x)^3 + 9^3:
(4 x)^3 + 9^3
Factor the sum of two cubes. (4 x)^3 + 9^3 = (4 x + 9) ((4 x)^2 - (4 x) 9 + 9^2):
(4 x + 9) ((4 x)^2 - 4 9 x + 9^2)
4×9 = 36:
(4 x + 9) ((4 x)^2 - 36 x + 9^2)
Multiply each exponent in 4 x by 2:
(4 x + 9) (4^2 x^2 - 36 x + 9^2)
4^2 = 16:
(4 x + 9) (16 x^2 - 36 x + 9^2)
9^2 = 81:
Answer: (4 x + 9) (16 x^2 - 36 x + 81)
Δ = b² - 4ac
Δ = (6)² - 4(2)(12)
Δ = 36 - 4(24)
Δ = 36 - 96
Δ = -60
y = 2x² + 6x + 12
0 = 2x² + 6x + 12
0 = 2(x²) + 2(3x) + 2(6)
0 = 2(x² + 3x + 6)
2 2
0 = x² + 3x + 6
x = -(3) ± √((3)² - 4(1)(6))
2(1)
x = -3 ± √(9 - 4(6))
2
x = -3 ± √(9 - 24)
2
x = -3 ± √(-15)
2
x = -3 ± i√(15)
2
x = -1.5 ± 0.5i√(15)
x = -1.5 + 0.5i√(15) or x = -1.5 - 0.5i√(15)
The discriminant is -60 and the number of solutions is 2.
Answer:
Correct Answer is B.) 4.8 units