Expert: Richard J. Raridon - 7/21/2009

Question
1.   How many solutions exist for a quadratic equation?  How do we determine algebraically whether the solutions are real or complex?


2.    What three techniques can be used to solve a quadratic equation?  Demonstrate these techniques on the equation "x2 - 10x - 39 = 0".


3.   



Look at the graph above and comment on the sign of D or the discriminant. Form the quadratic equation based on the information provided and find its solution.


4.   Translate the following into a quadratic equation, and solve it:  The length of a rectangular garden is four times its width; if the area of the garden is 196 square meters, what are its dimensions?



Last part of problems:




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

a)   x2 + 3x - 15 = 0
b)   x2 + x + 4 = 0
c)    x2 – 4x - 7  = 0
d)   x2 – 8x + 16 = 0
e)   2x2 - 3x + 7 = 0
f)   x2 – 4x - 77 = 0
g)   3x2 - 7x + 6 = 0
h)   4x2 + 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.  

Answer
1. 2, use quadratic equation
2. factor to get (x-13)(x+3) so that x = 13,-3
use quad. eq. x = [10 +/-(100+156)^1/2]/2 so x = 13,-3
complete the square x^2-10x+25 = 39+25
(x-5)^2 = 64 so x-5 = +/-8 and x = 5 +/-8 or x = 13, -3
3. no graph
4. L+4W and LW=196 so W = 7 and L = 28
1. a. irrational
b. imaginary
c. irrational
d. 2 identical answers
e. irrational
f. integers
g. imaginary
h. 2 identical
2. x^2-x-12=0
3. imaginary, like c or g above