Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $3 , i , - i$ and $P ( 2 ) = 30$
A) $P ( x ) = - 6 x ^ { 3 } + 18 x ^ { 2 } + 6 x - 18$
B) $P ( x ) = - 6 x ^ { 3 } + 18 x ^ { 2 } - 6 x + 18$
C) $P ( x ) = 6 x ^ { 3 } - 18 x ^ { 2 } + 6 x - 18$
D) $P ( x ) = 6 x ^ { 3 } - 18 x ^ { 2 } - 6 x + 18$

Question

Quizplus · Accepted Answer

The polynomial with zeros 3, i, and -i is $P(x) = a(x-3)(x-i)(x+i)$. Simplifying gives $P(x) = a(x-3)(x^2+1)$. Given $P(2) = 30$, solve for $a$: $a(2-3)(2^2+1) = 30$, which gives $a = -6$. Thus, $P(x) = -6(x-3)(x^2+1)$, which simplifies to $-6x^3 + 18x^2 - 6x + 18$.

Find a Polynomial of Degree 3 with Real Coefficients That 3,i,−i3 , i , - i3,i,−i

Find a Polynomial of Degree 3 with Real Coefficients That $3 , i , - i$