Degree 4 zeros 24 i 1 multiplicity 2 Enter the polynomial fx

Degree 4; zeros: -2+4 i; 1 multiplicity 2 Enter the polynomial. f(x) = a( )

Solution

zeros : x = -2 +4i

complex conjugate : x = -2 -4i

zeros : x = -1 multiplicity 2

f(x) = a( x+1)^2(x -2-4i)(x -2 +4i)

=a(x+1)^2(x^2 -2x +4ix - 2x+4 -8i -4ix +8i +16)

= a(x+1)^2(x^2 -2x+4 +16)

= a(x+1)^2(x^2 -2x +20)