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 -

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) (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 (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:

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None of the tutors are likely to do 8 problems in one submission. You give them a try, and email me via the thank you note for help, or to check your work.
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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
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