Answer:
x = [tex]\frac{3}{2} , -5[/tex]
Step-by-step explanation:
We know that we have to find the roots of the equation - which is another way of saying the x-intercepts, or the points that are on the x-axis that the graph passes through. All points on the x-axis have a y-value of 0. So, in order to find the roots for this equation, we need to find which values of x make the y equal 0.
The equation has already been factored out. So, we just need to find which values of x for each of the expressions in the parentheses will make the result 0. To do this, set the expressions in the parentheses to 0 and isolate x.
1) First, let's look at (2x-3). Write the equation 2x-3 = 0. Then, isolate x:
[tex]2x-3 = 0\\2x = 3\\x = \frac{3}{2}[/tex]
Therefore, [tex]\frac{3}{2}[/tex] is one of the roots.
2) Next, let's look at (x+5). Write the equation x+5 = 0. Then, isolate x:
[tex]x+5 = 0\\x = -5[/tex]
Therefore, -5 is a root as well.
The roots of the equation would be [tex]\frac{3}{2}[/tex] and -5.
