Solve the equation in the real number system.
-$x ^ { 3 } + 5 x ^ { 2 } + 2 x - 8 = 0$
A) {2, 4}
B) {-4, -2, 1}
C) {-4, -2}
D) {-1, 2, 4}

Question

Quizplus · Accepted Answer

To solve the cubic equation $x^3 + 5x^2 + 2x - 8 = 0$, we can try to find a real root by synthetic division or by inspection. Noticing that $x = 1$ is a root (since $1^3 + 5(1)^2 + 2(1) - 8 = 0$), we can divide the cubic polynomial by $x - 1$ to reduce it to a quadratic equation. The division gives us $x^2 + 6x + 8$, which factors further into $(x + 4)(x + 2)$. Therefore, the roots of the equation are $x = -4$, $x = -2$, and $x = 1$, matching option B.

Solve the Equation in the Real Number System x3+5x2+2x−8=0x ^ { 3 } + 5 x ^ { 2 } + 2 x - 8 = 0x3+5x2+2x−8=0

Solve the Equation in the Real Number System $x ^ { 3 } + 5 x ^ { 2 } + 2 x - 8 = 0$