Formulas for Polynomial

Question

The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=−3. The y-intercept is  y=−8.4;  Find a formula for P(x)P(x). 

Answer 1

roots 2 and -3

or

roots 2,2 and -3

a(x-2)^2(x+3)= -8.4 when x= 0

a = (0-2)^2(0+3) = -8.4

a(4)(3)=-8.4

a = -8.4/12 =-2.1/3 = -.7

-.7(x^2-4x +4)(x+3)

= -.7(x^3 +7x^2 -8x +12)

P(x) = -.7x^2 -4.9x^2 +5.6x -8.4

= the polynomial degree 3, with the given roots and y intercept