Question 164994: 1.) Determine whether the following equations have a solution or not? Justify your answer.
x^ + 6x - 7 = 0
z^ + z + 1 = 0
(3)1/2y^ - 4y - 7(3)1/2 = 0
2x^ - 10x + 25 = 0
2x^ - 6x + 5 = 0
s^ - 4s + 4 = 0
5/6x^ - 7x - 6/5 = 0
7a^ + 8a + 2 = 0
2.) 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.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first two to get you started
Remember,
If D>0 (ie the discriminant is positive), then you will have 2 real solutions,
If D=0, then you will have only 1 real solution, or
If D<0 (ie the discriminant is negative), then you will have 2 complex solutions (ie you will have NO real solutions).
a)
From  we can see that  ,  , and 
 Start with the discriminant formula.
 Plug in , , and
 Square  to get 
 Multiply  to get 
 Rewrite as
 Add to  to get 
Since the discriminant is greater than zero, this means that there are two real solutions.
b)
From  we can see that ,  , and 
Start with the discriminant formula.
 Plug in , , and
 Square  to get
 Multiply  to get 
 Subtract  from to get 
Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions.
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