Zeros of functions

Question

form a third degree polynomial with real coefficients such that -5+i and 1 are zeros

please show me the steps so that I can have an example of how to do this

Answer 1

You know you should have 3 zeros.  If the coefficients are real, then the complex conjugate of a complex zero must also be a zero.  Therefore, the 3 zeros are

 

1

-5 + i

-5 - i

 

p(x) = A(x - 1)[x - (-5 + i)][x - (-5 - i)]

 

where A is any real number ≠ 0.  You can expand p(x) to standard form if you wish, and see that the coefficients are real.