Agebra Problems
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Determine whether the following equations have a solution or not? Justify your answer. Problem:1. Determine whether the following equations have a solution or not? Justify your answer.
a) 5x2 + 8x + 7 = 0
b) (7)1/2y2 - 6y - 13(7)1/2 = 0
c) 2x2 + x - 1 = 0
d) 4/3x2 - ...there is moreshow problem1. Determine whether the following equations have a solution or not? Justify your answer.
a) 5x2 + 8x + 7 = 0
b) (7)1/2y2 - 6y - 13(7)1/2 = 0
c) 2x2 + x - 1 = 0
d) 4/3x2 - 2x + 3/4 = 0
e) 2x2 + 5x + 5 = 0
f) p2 - 4p + 4 = 0
g) m2 + m + 1 = 0
h) 3z2 + z - 1 = 0
2. If x = 3 and x = -5, then form a quadratic equation.
3. What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solution of the equation.
4. Create a real-life situation that fits into the equation (x + 3)(x - 4) = 0 and express the situation as the same equation.
Solve the following
1. A designer, attempting to arrange the characters of his artwork in the form of a square grid with equal number of rows and columns, found that 24 characters were left out. When he tried to add one more row and column, he found that he was short of 25 characters. Can you find the number of characters used by the designer?
2. Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?
3. Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
4. Rita rows 12 km upstream and 12 km downstream in 3 hours. The speed of her boat in still water is 9 km/hr. Find the speed of the stream.
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a) 5x2 + 8x + 7 = 0
D = b^2 - 4ac
= 64 - 140
= -76
Since D = -76 less than 0 no real solution exists.
b) (7)1/2y2 - 6y - 13(7)1/2 = 0
D = 36 + 364
= 400
Since D = 400 which is greater than 0 there are real solutions.
c) 2x2 + x - 1 = 0
D = 1 + 8
= 9
Since D = 9 which is greater than 0 there are real solutions.
d) 4/3x2 - 2x + 3/4 = 0
D = 4 - 4
= 0
Since D = 0, there is one solution.
e) 2x2 + 5x + 5 = 0
D = 25 - 40
= -15
Since D = -15 less than 0 no real solution exists.
f) p2 - 4p + 4 = 0
D = 16 - 16
= 0
Since D = 0, there is one solution.
g) m2 + m + 1 = 0
D = 1 - 4
= -3
Since D = -3 less than 0 no real solution exists.
h) 3z2 + z - 1 = 0
D = 1 + 12
= 13
Since D = 13 which is greater than 0 there are real ...
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