Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 5$ and $1 - i , P ( 0 ) = 10$
A) $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x$
B) $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x + 5$
C) $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 8 x + 10$
D) $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$

Question

Quizplus · Accepted Answer

Since the polynomial has real coefficients, the complex zeros must come in conjugate pairs. Thus, if $1 - i$ is a zero, so is $1 + i$. The polynomial can be constructed from its zeros as follows: $(x + 5)(x - (1 - i))(x - (1 + i))$. Simplifying this expression will eventually lead to the polynomial $x^3 + 3x^2 - 8x + 10$, which satisfies $P(0) = 10$.

Find a Polynomial of Degree 3 with Real Coefficients That −5- 5−5

Find a Polynomial of Degree 3 with Real Coefficients That $- 5$