SOLUTION: Form a polynomial f(x) with real coefficents having the given degree and zeros Degree 5; Zeros: 2; -i; -7+i Enter the polynomial f(x)=a(____) type expression using x as the varia

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Form a polynomial f(x) with real coefficents having the given degree and zeros Degree 5; Zeros: 2; -i; -7+i Enter the polynomial f(x)=a(____) type expression using x as the varia      Log On


   

Question 756608: Form a polynomial f(x) with real coefficents having the given degree and zeros
Degree 5; Zeros: 2; -i; -7+i
Enter the polynomial f(x)=a(____) type expression using x as the variable
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
+i and -7-i are also zeros because of -i and -7+i being zeros. You can begin forming your function using binomial factors this way:

f%28x%29=%28x-2%29%28x%2Bi%29%28x-i%29%28x-%28-7%2Bi%29%29%28x-%28-7-i%29%29

Next perform multiplications to achieve real coefficients when simplified, beginning with the binomial factors containing constant terms of conjugate complex pairs.

%28x%2Bi%29%28x-i%29=x%5E2%2B1
and


Writing the update for the function,
f%28x%29=%28x-2%29%28x%5E2%2B1%29%28x%5E2%2B14x%2B50%29 which is still not yet in the general form you want, but is still correct. Continue multiplying all the way if you want this in general form.