SOLUTION: 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)
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Question 199098: 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
any help would be appriciated.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first three to get you started (they all follow the same logic)
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)
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.
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