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Solutions of Quadratic Equations

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1.Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer.

a)x^2 + 3x - 15 = 0
b)x^2 + x + 4 = 0
c) x^2 - 4x - 7 = 0
d)x^2 - 8x + 16 = 0
e)2x^2 - 3x + 7 = 0
f)x^2 - 4x - 77 = 0
g)3x^2 - 7x + 6 = 0
h)4x^2 + 16x + 16 = 0

2.Find an equation for which -3 and 4 are solutions.

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 - 5) = 0 and express the situation as the same equation.

5.A rectangular garden has dimensions of 15 feet by 11 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 192 square feet?

6.A business invests $8,000 in a savings account for two years. At the beginning of the second year, an additional $2,500 is invested. At the end of the second year, the account balance is $11,445. What was the annual interest rate?

3.Steve traveled 150 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 2 hours less. Find the speed of his vehicle.

7.The Hudson River flows at a rate of 5 miles per hour. A patrol boat travels 40 miles upriver, and returns in a total time of 6 hours. What is the speed of the boat in still water?

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