SOLUTION: How do you write a quadratic equation with integer coefficients that could represent the following solution: x = -1 and x = 3

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Question 72237: How do you write a quadratic equation with integer coefficients that could represent the following solution:
x = -1 and x = 3
Found 2 solutions by rmromero, jim_thompson5910:
Answer by rmromero(383) About Me  (Show Source):
You can put this solution on YOUR website!



How do you write a quadratic equation with integer coefficients that could represent the following solution:



x = -1 and x = 3



Topic here is The sum and product of the Solutions



Find the sum of the solution.

      -1 + 3 = 2   the additive inverse for this will be the coeffient of 

                   the middle term. the additive inverse of 2 is -2



Find the product of the solution

      -1(3) = -3  the product will be the third term or the constant.



  x%5E2+-+%28s%5B1%5D%2Bs%5B2%5D%29x+%2B+%28s%5B1%5Ds%5B2%5D%29 



  x%5E2+-+%28-1%2B3%29x+%2B+%28-1%29%283%29



  x%5E2+-+2x+-3            -------> this is the quadratic equation





 

Rachel

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
When you are solving for x, you have the following form
pq=0Where p and q are factors of f(x). For instance p could equal (x-5) and q could equal (x+6). To solve for x, you set p and q equal to zero and isolate x. But this time you know what x is, you just need to find the factor that makes the polynomial. So if you have x=3 and x=-1, lets take x=3 first. What number adds to 3 to get 0? Well it would be -3. So in other words 3-3=0. If we replace the 1st 3 with x we get
x-3=0Theres one factor (if we plug in 3 for x, we get 0)
x%2B1=0There's the other factor, just do the same as before.
So now you multiply them together
%28x%2B1%29%28x-3%29FOIL
x%5E2-3x%2Bx-3
x%5E2-2x-3Thats the polynomial with roots of x=-1 and x=3
Check:
x%5E2-2x-3=0Plug in x=-1
%28-1%29%5E2-2%28-1%29-3=0
1%2B2-3=0
3-3=0
0=0Works
x%5E2-2x-3=0Plug in x=3
%283%29%5E2-2%283%29-3=0
9-6-3=0
3-3=0
0=0Works
It turns out in a product of factors
%28x%2Ba%29%28x%2Bb%29 The roots are x=-a and x=-b. Just a note for quick reference. So if you have any two roots, you can go backwards to get the equation.