Solve by quadratic formula: $3 x ^ { 2 } - 4 x + 3 = 0$
A) $\left\{ - \frac { 2 } { 3 } \pm \frac { \sqrt { 5 } } { 3 } \right\}$
B) none of these
C) $\left\{ \frac { 2 } { 3 } \pm \frac { \sqrt { 5 } } { 3 } i \right\}$
D) $\left\{ \frac { 2 } { 3 } \pm \frac { 2 \sqrt { 5 } } { 3 } i \right\}$

Question

Quizplus · Accepted Answer

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For $3x^2 - 4x + 3 = 0$, $a = 3$, $b = -4$, and $c = 3$. Plugging these into the formula gives $x = \frac{4 \pm \sqrt{(-4)^2 - 4(3)(3)}}{2(3)} = \frac{4 \pm \sqrt{16 - 36}}{6} = \frac{4 \pm \sqrt{-20}}{6} = \frac{2}{3} \pm \frac{\sqrt{20}}{6}i$. Simplifying $\sqrt{20}$ to $2\sqrt{5}$ gives $\frac{2}{3} \pm \frac{2\sqrt{5}}{6}i$, which simplifies further to $\frac{2}{3} \pm \frac{\sqrt{5}}{3}i$, matching choice C.

Solve by Quadratic Formula 3x2−4x+3=03 x ^ { 2 } - 4 x + 3 = 03x2−4x+3=0

Solve by Quadratic Formula $3 x ^ { 2 } - 4 x + 3 = 0$