Find a polynomial $f ( x )$ of degree $3$ that has the indicated zeros and satisfies the given condition. $2,2 i , - 2 i ; f ( 1 ) = - 15$
A) $f ( x ) = 48 x ^ { 3 } - 9 x ^ { 2 } + 12 x - 24$
B) $f ( x ) = 2 x ^ { 3 } - 2 x ^ { 2 } + 2 x - 30$
C) $f ( x ) = 2 x ^ { 3 } + 2 x ^ { 2 } + 2 x - 30$
D) $f ( x ) = 3 x ^ { 3 } - 6 x ^ { 2 } + 12 x - 12$
E) $f ( x ) = 3 x ^ { 3 } - 6 x ^ { 2 } + 12 x - 24$

Question

Quizplus · Accepted Answer

The polynomial with roots 2, 2i, and -2i is $f(x) = a(x-2)(x-2i)(x+2i)$. Simplifying gives $f(x) = a(x-2)(x^2+4)$. Given $f(1) = -15$, solve for $a$ to find the correct polynomial.

Find a Polynomial f(x)f ( x )f(x) Of Degree 333 That Has the Indicated Zeros and Satisfies the Given Condition

Find a Polynomial $f ( x )$ Of Degree $3$ That Has the Indicated Zeros and Satisfies the Given Condition