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

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(52786) (Show Source): You can put this solution on YOUR website!
.

    p(x) = , 


or, which is the same,


    p(x) = .


Each root    generates, creates and produces the factor   of the polynomial.


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

RELATED QUESTIONS
The polynomial of degree 5, P ( x ) has leading coefficient 1, has roots of multiplicity... (answered by MathLover1)

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2... (answered by Alan3354)

The polynomial of degree 5, P(x) has a leading coefficient 1, has roots of multiplicity 2 (answered by stanbon)

The polynomial of degree 5, P(x) has a leading coefficient 1, has roots of multiplicity 2 (answered by MathLover1,Solver92311)

the polynomial degree 5 p(x) has a leading coefficient 1 has roots of multiplicity of 2... (answered by josgarithmetic)

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2... (answered by ikleyn)

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2... (answered by ikleyn,josgarithmetic,math_tutor2020)

The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2... (answered by MathLover1)