SOLUTION: What function has x-intercepts -2/7 and 5/3 ? I think the answer is y=21x^2-29x-10 but I'm really not sure if I know what I'm doing. Can someone please explain it to me? Thanks.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: What function has x-intercepts -2/7 and 5/3 ? I think the answer is y=21x^2-29x-10 but I'm really not sure if I know what I'm doing. Can someone please explain it to me? Thanks.      Log On


   

Question 118817: What function has x-intercepts -2/7 and 5/3 ? I think the answer is y=21x^2-29x-10 but I'm really not sure if I know what I'm doing. Can someone please explain it to me? Thanks.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer is absolutely correct!
Here's how I did it so you can compare with the method you used.
The x-intercepts (also known as the "zeros") are given as:
x%5B1%5D+=+-2%2F7 and x%5B2%5D+=+5%2F3
Since you know the x-intercepts, you can find the factors of the original equation.
If x+=+-2%2F7 then x%2B2%2F7+=+0 This is one of the factors.
If x+=+5%2F3 then x-5%2F3+=+0 This is the other factor.
To find the equation, just multiply these two factor and set equal to zero:
%28x%2B2%2F7%29%28x-5%2F3%29+=+0
x%5E2-%285%2F3%29x%2B%282%2F7%29x-10%2F21+=+0 Multiply through by the LCD of 21.
21x%5E2-35x%2B6x-10+=+0 Simplify.
21x%5E2-29x-10+=+0... et Voila!