SOLUTION: The Polynomial of degree 5,p(x) has leading coefficient 1, has roots of multiplicity 2 at x = 5 and x = 0, and a root of multiplicity 1 at x = -1 Find a possible Formula for p(x

Algebra ->  Finance -> SOLUTION: The Polynomial of degree 5,p(x) has leading coefficient 1, has roots of multiplicity 2 at x = 5 and x = 0, and a root of multiplicity 1 at x = -1 Find a possible Formula for p(x      Log On


   

Question 1132207: The Polynomial of degree 5,p(x) has leading coefficient 1, has roots of multiplicity 2 at x = 5 and x = 0, and a root of multiplicity 1 at x = -1
Find a possible Formula for p(x)



Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.
    p(x) = %28x-5%29%5E2%2Ax%5E2%2A%28x-%28-1%29%29, 


or, which is the same,


    p(x) = x%5E2%2A%28x-5%29%5E2%2A%28x%2B1%29.


Each root  alpha  generates, creates and produces the factor %28x-alpha%29  of the polynomial.


Under the given condition, such a polynomial is unique: there is no other with the given properties.