SOLUTION: If you have a polynomial that has roots at -2 (single root), 1 (double root) and 3 (single root), what is the exact equation of the polynomial passing through the point (-4,210)?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: If you have a polynomial that has roots at -2 (single root), 1 (double root) and 3 (single root), what is the exact equation of the polynomial passing through the point (-4,210)?       Log On


   

Question 562138: If you have a polynomial that has roots at -2 (single root), 1 (double root) and 3 (single root), what is the exact equation of the polynomial passing through the point (-4,210)?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The polynomial must have factors x-%28-2%29=x%2B2,
%28x-1%29%5E2, and x-3.
If it is a polynomial of degree 4, it will be
P%28x%29=a%28x%2B2%29%28x-1%29%5E2%28x-3%29
If we also know that P%28-4%29=210
,
then a=210%2F350=3%2F5
P%28x%29=%283%2F5%29%28x%2B2%29%28x-1%29%5E2%28x-3%29=%283%2F5%29%28x%5E4-3x%5E3-3x%5E2%2B11x-6%29
There are also infinite other polynomials with the same roots passing through the same point. For example,
G%28x%29=%283%2F10%29%28x%5E2%2B4%29%28x%2B2%29%28x-1%29%5E2%28x-3%29 has exactly the same roots and complies with G%28-4%29=210, but its degree is 6,and it's probably not the intended answer.