Question

a1.Find the equation for a polynomial f(x) that satisfies the following:Degree 5Root of multiplicity 1 at x = 3• Root of multiplicity 2 at x = 2• Root of multiplicity 2 at x = -3y-intercept of (0, -216)f(x) =

Answer 1

we have that

the polynomial is of the form

f(x)=a(x-3)(x-2)^2(x+3)^2

where

a is the leading coefficient

y-intercept -----> (0,-216)

For x=0

substitute and solve for a

-216=a(0-3)(0-2)^2)(0+3)^2

-216=a(-3)(-2)^2(3)^2

-216=a(-3)(4)(9)

-216=-108a

a=2

therefore

`f(x)=2(x-3)(x-2)^2(x+3)^2`