SOLUTION: Please help! I went through my book and can not find examples for this Find the nth-degree polynomial function with real coefficients satisfying the given conditions: n=3;4 and

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help! I went through my book and can not find examples for this Find the nth-degree polynomial function with real coefficients satisfying the given conditions: n=3;4 and      Log On


   

Question 1040781: Please help! I went through my book and can not find examples for this
Find the nth-degree polynomial function with real coefficients satisfying the given conditions:
n=3;4 and 2i are zeros; f(-1)= -50
Found 2 solutions by Fombitz, MathDaddy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Real coefficients means complex roots come in complex conjugate pairs.
f%28x%29=%28x-3%29%28x-4%29%28x-2i%29%28x%2B2i%29 would be the solution for n=4, the lowest degree to satisfy the conditions.
f%28x%29=x%5E4-7x%5E3%2B16x%5E2-28x%2B48
.
.
.
For the general case,
f%28x%29=%28x-3%29%5Ei%2A%28x-4%29%5Ej%2A%28x%5E2%2B4%29%5Ek
where i,j,k are all positive integers which leads to a degree of
n=i%2Bj%2B2k

Answer by MathDaddy(1) About Me  (Show Source):
You can put this solution on YOUR website!
(n-3)(n-4)(n-2i)(n+2i). Complex conjugates.
FOIL out the pairs, distribute n squared and the 4. You get
+f%28x%29=n%5E4-7n%5E3%2B16n%5E2-28n%2B48
Now, f(-1) will equal 100.
So multiply each term by negative half.