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.



   



  



              -------> this is the quadratic equation





 

Rachel 

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
 When you are solving for x, you have the following form

Where 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

Theres one factor (if we plug in 3 for x, we get 0)

There's the other factor, just do the same as before.

So now you multiply them together

FOIL



Thats the polynomial with roots of x=-1 and x=3

Check:

Plug in x=-1







Works

Plug in x=3







Works

It turns out in a product of factors

 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.



 

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