SOLUTION: Hello, Can someone help me with the following: 1. write a quadratic equation having the given numbers as solutions 5, only solution 2. complete the square. then wri

Algebra ->  Equations -> SOLUTION: Hello, Can someone help me with the following: 1. write a quadratic equation having the given numbers as solutions 5, only solution 2. complete the square. then wri      Log On


   

Question 245918: Hello,
Can someone help me with the following:
1. write a quadratic equation having the given numbers as solutions
5, only solution
2. complete the square. then write the trinomial square in factored form.
x^2-3x
3. solve by applying the quadratic formula
2x^2+7x+3=0
4. use the discriminant to determine whether the following equations have solutions that are two different rational solutions; two different irrational solutions; exactly one rational solution, or two different imaginary solutions.
10-5a^2=7a+9

I have been out of school for 15 years and I am not doing well in this class if you can help me I really would appreciate it. I know that you all are great at helping people like me.
Please help me.
Thank you,

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. write a quadratic equation having the given numbers as solutions
5, only solution
(x-5)*(x-5) = 0
x%5E2+-+10x+%2B+25+=+0
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2. complete the square. then write the trinomial square in factored form.
x^2-3x
x^2 - 3x + 2.25
= (x - 1.5)^2
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3. solve by applying the quadratic formula
2x^2+7x+3=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B7x%2B3+=+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=%287%29%5E2-4%2A2%2A3=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+25+%29%29%2F2%5C2+=+-0.5
x%5B2%5D+=+%28-%287%29-sqrt%28+25+%29%29%2F2%5C2+=+-3

Quadratic expression 2x%5E2%2B7x%2B3 can be factored:
2x%5E2%2B7x%2B3+=+%28x--0.5%29%2A%28x--3%29
Again, the answer is: -0.5, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B7%2Ax%2B3+%29

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4. use the discriminant to determine whether the following equations have solutions that are two different rational solutions; two different irrational solutions; exactly one rational solution, or two different imaginary solutions.
10-5a^2=7a+9
5a^2 + 7a - 1 = 0
The online solver covers the Discriminant well.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B7x%2B-1+=+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=%287%29%5E2-4%2A5%2A-1=69.

Discriminant d=69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+69+%29%29%2F2%5C5+=+0.130662386291807
x%5B2%5D+=+%28-%287%29-sqrt%28+69+%29%29%2F2%5C5+=+-1.53066238629181

Quadratic expression 5x%5E2%2B7x%2B-1 can be factored:
5x%5E2%2B7x%2B-1+=+%28x-0.130662386291807%29%2A%28x--1.53066238629181%29
Again, the answer is: 0.130662386291807, -1.53066238629181. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B7%2Ax%2B-1+%29