Solve the radical equation, and check all proposed solutions.
-$$2 x - 5 = 18 x ^ { 3 } - 45 x ^ { 2 }$$
A) $\left\{ - \frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 5 } { 2 } \right\}$
B) $\left\{ 0 , \frac { 5 } { 2 } \right\}$
C) $\left\{ - \frac { 1 } { 9 } , \frac { 1 } { 9 } , \frac { 5 } { 2 } \right\}$
D) $\left\{ - \frac { 1 } { 3 } , \frac { 1 } { 3 } , \frac { 2 } { 5 } \right\}$

Question

Quizplus · Accepted Answer

First, rearrange the equation to set it to zero: $18x^3 - 45x^2 - 2x + 5 = 0$. Factoring out common terms and solving the cubic equation, we find the roots to be $-\frac{1}{3}$, $\frac{1}{3}$, and $\frac{5}{2}$.

Solve the Radical Equation, and Check All Proposed Solutions 2x−5=18x3−45x22 x - 5 = 18 x ^ { 3 } - 45 x ^ { 2 }2x−5=18x3−45x2

Solve the Radical Equation, and Check All Proposed Solutions $2 x - 5 = 18 x ^ { 3 } - 45 x ^ { 2 }$