SOLUTION: 1. Determine whether the following equations have a solution or not? Justify your answer.
a) x^2 + 6x - 7 = 0
b) z^2 + z + 1 = 0
c) (3)^(1/2)*y^2 - 4y - 7*(3)^(1/2) = 0
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Question 155165: 1. Determine whether the following equations have a solution or not? Justify your answer.
a) x^2 + 6x - 7 = 0
b) z^2 + z + 1 = 0
c) (3)^(1/2)*y^2 - 4y - 7*(3)^(1/2) = 0
d) 2x^2 - 10x + 25 = 0
e) 2x^2 - 6x + 5 = 0
f) s^2 - 4s + 4 = 0
g) (5/6)x^2 - 7x - 6/5 = 0
h) 7a^2 + 8a + 2 = 0
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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.
-----------------------------------------------
c)
^{\frac{1}{2}})
Start with the given expression
Rewrite 
as
From , we can see that , , and
Start with the discriminant formula
Add
Since the discriminant is greater than zero, this means that there are two real solutions.
---------------------------------------------
d)
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.
--------------------------------------------------------------------
e)
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.
-----------------------------------------------------------------
f)
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 equal to zero, this means that there is one real solution.
------------------------------------------------------------------------
g)
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.
------------------------------------------------------------------
h)
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 greater than zero, this means that there are two real solutions.
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