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=-11.2; find a formula for P(x)

Question

Thank you!!

Answer 1

root x=4, multiplicity 2:  (x-4)²

root x=1, multiplicity 1:  (x-1)

 

p(x) = a(x-4)²(x-1) where a is some number

 

y-intercept -11.2 so p(0) = -11.2

 

a(0-4)²(0-1) = -11.2

a(16)(-1) = -11.2

-16a = -11.2

a = -11.2/(-16)

a= 11.2/16

 

p(x) = (11.2/16)(x-4)²(x-1)