Form a polynomial f(x) with the real coefficients having the given degree and zeros.

Question

Degree 5; Zeros: -3; -i; -6+i

f(x)=a( )

Answer 1

If the zeroes are a1,a2,a3, etc. then the polynomial is:

p(x) = A (x-a1)(x-a2)(x-a3)....

If all the coefficients are real, then the zeroes come in pairs of complex conjugates. So, in this problem it is given that -i is a zero, and then it follows that i is also a zero.

Answer 2

So then a=0?

Answer 3

What would be the polynomial?