The polynomial of degree 4 Px has a squareroot of multiplici

The polynomial of degree 4, P(x) has a squareroot of multiplicity 2 at x = 4 and squareroots of multiplicity 1 at x = 0 and x = -2. Its lead coefficient is 4. Find a formula for P(x).

Solution

roots of multiplicity 2 at x=4 ----> (x-4)^2

roots of multiplicity 1 at x=0 -----> (x -0)

roots of multiplicity 1 at x=-2 -----> (x +2)

The coefficient P(x) = kx(x-4)^2( x+2)

k is the lead coefficient =4

P(x) = 4x(x-4)^2(x+2)