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

Question

Degree 5; zeros: 4; -i, -7+i

Enter the polynomial

f(x)=a( __ + __ - __ - ___ - __- ___)

Answer 1

WE using Conjugate zeros theorem: complex zerose can be only as congugate pair if polynomial with real coefficients. We have 5 zeros: 4, -i, i, -7 + i, -7 - i.

Polynomial what we looking for in factored form: a(x - 4)(x-i)(x+i)(x +7 - i)(x - 7 + i) = a(x-4)(x²+1)(x² +14x + 50), where a ≠ 0 any real number.