Solve the equation exactly in the complex number system.
-$$x ^ { 3 } + 2 x ^ { 2 } + 49 x + 98 = 0$$
A) $x = - 2 , x = 98 i , x = 49 i$
B) $x = - \sqrt { 2 } , x = \pm 7 i$
C) $x = - 2 , x = \pm \sqrt { 7 }$
D) $x = - 2 , x = \pm 7 i$

Question

Quizplus · Accepted Answer

First, factor out the equation: $x^3 + 2x^2 + 49x + 98 = 0$ can be factored as $(x + 2)(x^2 + 49) = 0$. Solving $x + 2 = 0$ gives $x = -2$. Solving $x^2 + 49 = 0$ gives $x^2 = -49$, which leads to $x = \pm 7i$.

Solve the Equation Exactly in the Complex Number System x3+2x2+49x+98=0x ^ { 3 } + 2 x ^ { 2 } + 49 x + 98 = 0x3+2x2+49x+98=0

Solve the Equation Exactly in the Complex Number System $x ^ { 3 } + 2 x ^ { 2 } + 49 x + 98 = 0$