Use the factoring method to solve the equation. $6 x ^ { 2 } + 13 x + 5 = 0$
A) $- \frac { 1 } { 2 }$ , $- \frac { 5 } { 3 }$
B) $\frac { 5 } { 3 }$ , $\frac { 1 } { 2 }$
C) $- \frac { 5 } { 3 }$ , $\frac { 1 } { 2 }$
D) $- \frac { 1 } { 2 }$ , $\frac { 1 } { 2 }$
E) $- \frac { 1 } { 2 }$ , $\frac { 5 } { 3 }$

Question

Quizplus · Accepted Answer

To factor the quadratic equation $6x^2 + 13x + 5 = 0$, we look for two numbers that multiply to $6 \times 5 = 30$ and add to 13. These numbers are 10 and 3. Rewriting the middle term, we get $6x^2 + 10x + 3x + 5 = 0$. Factoring by grouping, we have $2x(3x + 5) + 1(3x + 5) = 0$, leading to $(2x + 1)(3x + 5) = 0$. Setting each factor equal to zero gives $x = -\frac{1}{2}$ and $x = -\frac{5}{3}$.

Use the Factoring Method to Solve the Equation 6x2+13x+5=06 x ^ { 2 } + 13 x + 5 = 06x2+13x+5=0

Use the Factoring Method to Solve the Equation $6 x ^ { 2 } + 13 x + 5 = 0$