B With degree 4 roots with multiplicity 1 at x 3 and x 0 a

B) With degree 4, roots with multiplicity 1 at x = 3 and x = 0 and multiplicity 2 at x = -2, and going through the point (1, -6).

roots with multiplicity 1 at x = 3 and x = 0 and multiplicity 2 at x = -2,

Let f(x) = a*(x -3)x(x-2)^2

= ax(x -3)(x -2)^2

It passes through ( 1, -6)

-6 = a*1(1 -3)( 1-2)^2

-6 = a*(-2)(1)

a = 3

So, f(x) =3x(x -3)(x -2)^2