The polynomial of degree 5, P(x) has leading coefficient 1, has roots of multiplicity 2 at x=1 and x=0, and a root of multiplicity 1 at x=-1 Find a possible formula for P(x)?
1 Answer
Feb 8, 2018
# P(x) = x^2(x-1)^2(x+1) #
Explanation:
Given that we have a root of multiplicity
Given that we have a root of multiplicity
Given that we have a root of multiplicity
We are given that
# P(x) = 0 => x^2(x-1)^2(x+1) = 0 #
And we can therefore write
# P(x) = Ax^2(x-1)^2(x+1) #
We also know that the leading coefficient is
Hence,
# P(x) = x^2(x-1)^2(x+1) #