Download Week 1 Assignment 4: Mixed Problems

Week 5 Assignment 3: Mixed Problems
By Day 4 complete and submit your answers to the facilitator; please show all necessary
work. By Day 5 post your answers in the appropriate thread for review and comments
from others.
For questions 1-2, apply the quadratic formula to find the roots of the given function,
and then graph the function.
1. (6 points) f(x) = x2 - 4
X = (0 +/- sqrt(0^2-4*1*-4))/2
X = (+/- sqrt(16))/2
X = +/- 4 / 2
X = 2 or -2
2. (6 points) g(x) = x2 - x - 12
X = (1 +/- sqrt(1^2-4*1*-12))/2
X = (1 +/- sqrt(49))/2
X = (1 +/- 7)/2
X = 4 or -3
For questions 3-4, factor the quadratic expression completely, and find the roots of
the expression.
3. (3 points) 20x2 + 13x + 2
(4x+1)(5x+2) = 0
X = -1/4 or -2/5
4. (3 points) 49x2 - 14x - 3
(7x-3)(7x+1) = 0
X = 3/7 or -1/7
For question 5, complete the square, and find the roots of the quadratic equation.
5. (3 points) x2 + 16x = 0
x^2 + 16x + 64 = 64
(x+8)^2 = 64
x+8 = +/- 8
x = -8 +/- 8
x = -16 or 0
In questions 6-10, use the discriminant to determine the number of solutions of the
quadratic equation, and whether the solutions are real or complex. Note: It is not
necessary to find the roots; just determine the number and types of solutions.
6. (3 points) x2 + 6x - 7 = 0
6^2-4*1*-7 = 64, two real
7. (3 points) z2 + z + 1 = 0
1^2-4*1*1 = -3, two complex
8. (3 points) (3)1/2y2 - 4y - 7(3)1/2 = 0
4^2-4*sqrt(3)*-7*sqrt(3) = 100, two real
9. (3 points) 2x2 - 10x + 25 = 0
10^2-4*2*25 = -100, two complex
10. (3 points) 2x2 - 6x + 5 = 0
6^2-4*2*5 = -4, two complex
11. (5 points) Steve traveled 200 miles at a certain speed. Had he gone 10mph faster,
the trip would have taken 1 hour less. Find the speed of his vehicle.
200/x – 1 = 200/(x+10)
Multiply by x(x+10):
200(x+10) – x(x+10) = 200x
200x + 2000 – x^2 – 10x = 200x
-x^2 – 10x + 2000 = 0
(x+50)(x-40) = 0
X = -50 or 40
Can’t be negative, so:
40 mph
12. (5 points) The Hudson River flows at a rate of 3 miles per hour. A patrol boat
travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of
the boat in still water?
60/(x+3) + 60/(x-3) = 9
Multiply by (x+3)(x-3):
60(x-3) + 60(x+3) = 9(x^2-9)
60x-180 + 60x + 180 = 9x^2 – 81
120x = 9x^2 – 81
9x^2 – 120x – 81 = 0
X = (120 +/- sqrt(120^2-4*9*-81))/18
X = (120 +/- sqrt(17316))/18
X = 13.977 or -0.644
It can’t be negative, so:
13.977 mph
13. (5 points) A designer attempts to arrange the characters of his artwork in the
form of a square grid with equal numbers of rows and columns, but finds that 24
characters are left out. When he tries to add one more row and column, he finds that
he has 25 too few characters. Find the number of characters used by the designer.
x^2 + 24 = (x+1)^2 – 25
x^2 + 24 = x^2 + 2x + 1 – 25
24 = 2x – 24
48 = 2x
X = 24
X^2 = 576 used in the grid + 24 leftover
= 600 total characters