Find all solutions real and complex of the equation x2-4x50

Question

Assignment

1. Solve using the Quadratic formula: x³ - 4x - 4 = 0.
A. 2
B. 2±2√2
C. 2±4√2
D. 4±2√2

2. Solve the equation: 9x⁴ - 10x² + 1 = 0
A. 1/3, 1
B. ±1/3, ±1
C. 1/9, 1
D. ±1/3

3. Solve the rational equation: (3/2) - {1/(x-4)} = -2/(2x - 8).
A. x = 4
B. x = -4
C. x = 0
D. No solution

4. Solve the rational equation: {1/(x-2)} + {1 / (x -3) = 2 / (x - 2) (x - 3)
A. 2
B. 3
C. 4
D. 5

5. Solve the inequality.  x2 - 6x ≤ 27
Write the solution using interval notation: 5.
A. (-3, 9)
B. (-∞, -3] ∪ [9, ∞)
C. [-3, 9]
D.[-9, 3]

6. Find the minimum or maximum value of f(x) = -x² + 6x - 5, and give the coordinates of the vertex of the parabola.
A. Maximum = 3; vertex (3, 4)
B. Maximum = 4; vertex (4, 3)
C. Minimum = 4; vertex
D. None of the above

7. Find the Vertex and indicate the direction that the parabola opens: f(x) = x² - 2x + 4
A. Vertex and Opens Up.
B. Vertex and Opens Up.
C. Vertex and Opens Down.
D. Vertex and Opens Down.

8. Simplify: i⁵
A. 1
B. -1
C. i
D. -i

9. Multiply: .
A.
B. 7
C.
D.

10. Express in the standard form a + bi: 5i / (1 + 2i)
A. (2/5) + (1/5)i
B. 2 + i
C. (1/5) - (2/5)i
D. 2 - i

11. Find the Vertical Asymptote: f(x) = (4 -x) / (2 + x)
A. x=2
B. x=-2
C. x=-4
D. x=4

12. Find the Horizontal Asymptote: f(x) = (4 -x) / (2 + x)
A. x=2
B. x=-2
C. x=-1
D. x=1

13. Let f (x) = -2x³+4x²-x+1. Use the Intermediate Value Theorem to determine which interval must contain a zero of f(x).
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4

14. True or False: Let y=f(x) be a polynomial function. The x-intercepts of the function f(x) are the roots of the equation f(x) = 0.

15. True or False. Let y=f(x) be a polynomial function of degree 3.
The function y=f(x) must have at least one real root.

16. True or False. It is possible for a quadratic equation with real coefficients to have one real and one complex root.

17. Consider the graph of the polynomial y=p(x). Answer the following questions. (No explanation needed)

(a) Is the degree of p(x) even or odd?
(b) Is the leading coefficient positive or negative?
(c) How many real number zeros are there?

18. Let f(x) = (2x² - 2) / (x² - 4) (No explanations required)
(a) State the y-intercept.
(b) State the x-intercept(s).
(c) State the vertical asymptote(s).
(d) State the horizontal asymptote.
(e) Draw the graph. Show the asymptotes.

19. Translate this sentence about area into a mathematical equation.

The area A of a regular hexagon is directly proportional to the square of the length s of its side.

20. Find all solutions, real and complex, of the equation x²-4x+5=0.

Simplify as much as possible and clearly show all the steps.