A 5th degree polynomial function has zeros 01 multiplicity o

A 5th degree polynomial function has zeros 0.1 multiplicity of two, -4, 1/3 Create the polynomial function in factored form. A 3th degree polynomial function has zeros 0, i, -i. Create the polynomial function in factored form.

Solution

4) Roots give x= 0 ( multiplicity 1)

x=1 ( multiplicity 2)

x = 4 ; x= 1/3 ( multiplicity 1)

f(x) = x(x-1)^2(x -4)(x-1/3)

5) zeros : x=0 ; x= i ; x= -i

f(x) = x(x-i)(x +i)

= x(x^2 +1)