Solve the equation by the zero-factor property.
-$$6 x ^ { 2 } + 23 x + 21 = 0$$
A) $\left\{ \frac { 3 } { 2 } , \frac { 7 } { 3 } \right\}$

B) $\left\{ \frac { 2 } { 3 } , \frac { 3 } { 7 } \right\}$

C) $\left\{ - \frac { 2 } { 3 } , - \frac { 7 } { 3 } \right\}$

D) $\left\{ - \frac { 3 } { 2 } , - \frac { 7 } { 3 } \right\}$

Question

Solve the equation by the zero-factor property.
-$$6 x ^ { 2 } + 23 x + 21 = 0$$
A) $\left\{ \frac { 3 } { 2 } , \frac { 7 } { 3 } \right\}$

B) $\left\{ \frac { 2 } { 3 } , \frac { 3 } { 7 } \right\}$

C) $\left\{ - \frac { 2 } { 3 } , - \frac { 7 } { 3 } \right\}$

D) $\left\{ - \frac { 3 } { 2 } , - \frac { 7 } { 3 } \right\}$

Quizplus · Accepted Answer

To solve the quadratic equation $6x^2 + 23x + 21 = 0$ using the zero-factor property, we first need to factor the quadratic if possible. Factoring this equation directly might be challenging, so we can use the quadratic formula instead, where $a = 6$, $b = 23$, and $c = 21$. The solutions from the quadratic formula are $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. Substituting the values gives $$x = \frac{-23 \pm \sqrt{(23)^2 - 4(6)(21)}}{2(6)}$$, which simplifies to $$x = \frac{-23 \pm \sqrt{529 - 504}}{12}$$, and further to $$x = \frac{-23 \pm \sqrt{25}}{12}$$. This gives the solutions $$x = \frac{-23 + 5}{12}$$ and $$x = \frac{-23 - 5}{12}$$, which simplify to $$x = -\frac{3}{2}$$ and $$x = -\frac{7}{3}$$. Therefore, the correct answer is $\left\{ - \frac { 3 } { 2 } , - \frac { 7 } { 3 } \right\}$.

Solve the Equation by the Zero-Factor Property 6x2+23x+21=06 x ^ { 2 } + 23 x + 21 = 06x2+23x+21=0

Solve the Equation by the Zero-Factor Property $6 x ^ { 2 } + 23 x + 21 = 0$