The polynomial of degree 3, P( x ), has a root of multiplicity 2 at x = 4 and a root of multiplicity 1 at x = − 1. The y -intercept is y = − 6.4. Find a formula for P ( x ). P ( x ) =

Answer 1

P(x) = a(x+1)(x-4)^2

= a(x+1)(x^2 - 8x + 16)

= a(x^3 -7x^2 +8x +16)

=a(x^3 -7x^2 + 8x) + 16a

where 16a = -6.4,

a = -6.4/16

a = -.4

P(x) = -.4(x^3 -7x^2 + 8x + 16)

P(x) = -.4x^3 +2.8x^2 -3.2x -6.4 is the 3rd degree polynomial with the given roots and y intercept