College Algebra help please! (3rd degree polynomial)
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College Algebra help please! (3rd degree polynomial)

[From: ] [author: ] [Date: 11-12-14] [Hit: ]
..if i is a zero, then - i is too !now,so,......
This is for review for my final exam. I would like to learn how to grasp the concept and answer the problem correctly, so please explain each step.


Find a 3rd degree polynomial function with real coefficients satisfying the given conditions.

-4 and i are zeros; f(2) = 90

thank you in advance & will choose best answer!

-
complex/imaginary solutions come in conjugate pairs...if " i " is a zero, then " - i " is too !

f(x) = a(x + 4)(x + i_)(x - i) = a(x + 4)(x^2 + 1) = a(x^3 + 4x^2 + x + 4)

now, solve for a: you know that f(2) = 90

so,

f(2) = 90 = a(x^3 + 4x^2 + x + 4) = a(8 + 16 + 2 + 4) = a(30)

a = 3

the funciton is: f(x) = 3x^3 + 12x^2 + 3x + 4

check

qed
1
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