Question

Calcule la suma de todas las raíces de $\begin{aligned} &(2x+3)(x-4) \\ &\quad {}+(2x+3)(x-6)=0. \end{aligned}$

Compute the sum of all the roots of $\begin{aligned} &(2x+3)(x-4) \\ &\quad {}+(2x+3)(x-6)=0. \end{aligned}$

$\dfrac{7}{2}$

$4$

$5$

$7$

$13$

Al factorizar $2x+3$ se obtiene $(2x+3)\big[(x-4)+(x-6)\big]$ $= (2x+3)(2x-10)$ $= 0.$

Las raíces son $-\dfrac{3}{2}$ y $5,$ cuya suma es $-\dfrac{3}{2} + 5 = \dfrac{7}{2}.$

Por lo tanto, la respuesta correcta es A.

Factoring out $2x+3$ gives $(2x+3)\big[(x-4)+(x-6)\big]$ $= (2x+3)(2x-10)$ $= 0.$

The roots are $-\dfrac{3}{2}$ and $5,$ whose sum is $-\dfrac{3}{2} + 5 = \dfrac{7}{2}.$

Thus, the correct answer is A.