Form a polynomial fx with real coefficients having the given

Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 5; zeros: 6; -i; 3+i

answer: f(x)=a( )

Degree 5-----> means five roots

Given : zeros given: 6; -i; 3+i

x = 6 ; x= -i .If there is a complex root, roots will be pair of complex conjugate

x = -i other root would +i

Similarly for x = 3+i other root would be 3- i

So , f(x) = a(x-6)(x+i)(x-i)(x -3 - i)(x -3+i)

= a(x-6)(x^2 +1)(x^2 -3x +ix -3x+9 -3i -ix +3i +1)

f(x) =a (x-6)(x^2 +1)( x^2 -6x +10)