SOLUTION: 1. Determine whether the following equations have a solution or not? Justify your answer. a) x2 + 3x - 15 = 0 b) x2 + x + 4 = 0 c) x2 – 4x - 7 = 0 d) x2 – 8x + 16 = 0

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Question 181251: 1. Determine whether the following equations have a solution or not? 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
I do not understand this one. Please help.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Determine whether the following equations have a solution or not? 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
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All quadratics have solutions. The solution might not be real numbers, but they're still solutions.
For example:
a) x2 + 3x - 15 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=69 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.65331193145904, -5.65331193145904. Here's your graph:

This has real number solutions, tho the numbers are irrational.
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b) x2 + x + 4 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -15 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -15 is + or - .

The solution is , or
Here's your graph:

The solutions are complex numbers, but they are solutions.
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