SOLUTION: Can you help me solve this question? Determine the number of solutions and classify the type of solutions for each of the following equations. Justify the answers. a. x^2 + 3x -

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Question 203923: Can you help me solve this question?
Determine the number of solutions and classify the type of solutions for each of the following equations. Justify the answers.
a. x^2 + 3x - 15 = 0
b. x^2 + x + 4 = 0
c. sqrt2^2 - 4x - 7 sqrt2 = 0
d. x^2 - 8x + 16 = 0
e. 2x^2 - 3x + 7 = 0
f. x^2 - 4x - 77 =0
g. 3x^2 - 7x + 6 = 0
h. 4x^2 + 16x + 16= 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Determine the number of solutions and classify the type of solutions for each of the following equations. Justify the answers.
a. x^2 + 3x - 15 = 0
This is well covered by the onsite solver. Read the info about the discriminant.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-15+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A-15=69.

Discriminant d=69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+69+%29%29%2F2%5C1+=+2.65331193145904
x%5B2%5D+=+%28-%283%29-sqrt%28+69+%29%29%2F2%5C1+=+-5.65331193145904

Quadratic expression 1x%5E2%2B3x%2B-15 can be factored:
1x%5E2%2B3x%2B-15+=+%28x-2.65331193145904%29%2A%28x--5.65331193145904%29
Again, the answer is: 2.65331193145904, -5.65331193145904. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-15+%29

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b. x^2 + x + 4 = 0
c. sqrt2^2 - 4x - 7 sqrt2 = 0
d. x^2 - 8x + 16 = 0
e. 2x^2 - 3x + 7 = 0
f. x^2 - 4x - 77 =0
g. 3x^2 - 7x + 6 = 0
h. 4x^2 + 16x + 16= 0