SOLUTION: Write a quadratic equation with the solutions (-3,1) in the form of ax^2+bx+c=0. I thought it was x^2-4x+3=0. I don't think this is right, can someone show me what I am doing wro

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Write a quadratic equation with the solutions (-3,1) in the form of ax^2+bx+c=0. I thought it was x^2-4x+3=0. I don't think this is right, can someone show me what I am doing wro      Log On


   

Question 279384: Write a quadratic equation with the solutions (-3,1) in the form of ax^2+bx+c=0.
I thought it was x^2-4x+3=0.
I don't think this is right, can someone show me what I am doing wrong? Please!
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Why don't you think it is right?
It has the right form!
The middle term has to be the sum of 3 and -1
(x+3)(x-1)=0
FOIL
x^2
-1x
+3x
-3
x^2+2x-3=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-3+=+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=%282%29%5E2-4%2A1%2A-3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+1
x%5B2%5D+=+%28-%282%29-sqrt%28+16+%29%29%2F2%5C1+=+-3

Quadratic expression 1x%5E2%2B2x%2B-3 can be factored:
1x%5E2%2B2x%2B-3+=+1%28x-1%29%2A%28x--3%29
Again, the answer is: 1, -3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-3+%29