Solve the problem.
-Solve the equation $8 x ^ { 3 } - 42 x ^ { 2 } + 43 x - 12 = 0$ given that $\frac { 1 } { 2 }$ is a root.
A) $\left\{ \frac { 1 } { 2 } , \frac { 3 } { 4 } , 4 \right\}$
B) $\left\{ \frac { 1 } { 2 } , - \frac { 3 } { 4 } , - 4 \right\}$
C) $\left\{ \frac { 1 } { 2 } , 1,3 \right\}$
D) $\left\{ \frac { 1 } { 2 } , - 1 , - 3 \right\}$

Question

Quizplus · Accepted Answer

Given that $\frac{1}{2}$ is a root, we can use synthetic division or polynomial division to divide the polynomial by $x - \frac{1}{2}$. This process simplifies the equation to a quadratic, which can then be solved using the quadratic formula or factoring. The roots of the resulting quadratic equation are $\frac{3}{4}$ and $4$, making the complete set of solutions $\left\{ \frac{1}{2}, \frac{3}{4}, 4 \right\}$.

Solve the Problem 8x3−42x2+43x−12=08 x ^ { 3 } - 42 x ^ { 2 } + 43 x - 12 = 08x3−42x2+43x−12=0

Solve the Problem $8 x ^ { 3 } - 42 x ^ { 2 } + 43 x - 12 = 0$