Find a formula for P(x)

Question

The polynomial of degree , , has a root of multiplicity  at  and a root of multiplicity  at . The -intercept is  . Find a formula for . 

Answer 1

1 is a root of multiplicity 2 and -2 is a root of multiplicity 1. So, the general form of the polynomial is

y=a(x+2)(x-1)²

We now need to find the value of a. It is given that the y intercept is -0.6. So, y(0)=-0.6.

Substituting in the above equation,

-0.6=a(0+2)(0-1)²

-0.6=2a

-0.3=a

so, the polynomial is P(x)=-0.3(x+2)(x-1)²