Solve the equation by using the quadratic formula.
-$( 3 w - 2 ) ( w - 1 ) = - 3$
A) $\left\{ \frac { 5 } { 6 } - \frac { \sqrt { 35 } } { 6 } i , \frac { 5 } { 6 } + \frac { \sqrt { 35 } } { 6 } i \right\}$
B) $\left\{ - \frac { 5 } { 6 } - \frac { \sqrt { 37 } } { 6 } i , \frac { 5 } { 6 } + \frac { \sqrt { 37 } } { 6 } i \right\}$
C) $\left\{ - \frac { 1 } { 3 } , - 2 \right\}$
D) $\left\{ \frac { - 5 - \sqrt { 35 } } { 6 } , \frac { - 5 + \sqrt { 35 } } { 6 } \right\}$

Question

Quizplus · Accepted Answer

First, expand and simplify the given equation: $3w^2 - 5w + 2 = -3$. Adding 3 to both sides gives $3w^2 - 5w + 5 = 0$. Using the quadratic formula, $w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 3$, $b = -5$, and $c = 5$, yields complex roots, which match choice A.

Solve the Equation by Using the Quadratic Formula (3w−2)(w−1)=−3( 3 w - 2 ) ( w - 1 ) = - 3(3w−2)(w−1)=−3

Solve the Equation by Using the Quadratic Formula $( 3 w - 2 ) ( w - 1 ) = - 3$