SOLUTION: "Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the rea

Question 528299: "Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3; -3 and 6+2i are zeros; f(2)=100
f(x)= ?
Thank you!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
complex roots (zeros containing i's) occur in conjugate pairs; if 6+2i is a zero, then 6-2i is also

if "r" is a root (zero) of a function, then "x-r" is a factor

f(x) = a(x - 3)(x - 6 - 2i)(x - 6 + 2i) = a(x - 3)(x^2 - 12x + 40)

use f(2)=100 to find the value of "a"
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