Find a formula for P ( x ) .

Question

The polynomial of degree 4,  has a root of multiplicity 2 at  and roots of multiplicity 1 at  and . It goes through the point .

Find a formula for .

Answer 1

since you have a multiplicity of 2at x=3 this gives you a factor of (x-3)^2

The single multiplicities give you factors of c and (x+3) so equation is

y =a(x-3)^2(x)(x+3). Use the point (5,112) to solve for a

a(5-3)^2(5)(5+3)=112

a(4)(5)(8)=112

a=7/10 or .7 so final equation is

y=.7(x-3)^2(x)(x+3)