Question

Find the roots for y = (2x-3)(x+5) (The x values)

Answer 1

x =
`(3)/(2) , -5`

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:

`2x-3 = 0\\2x = 3\\x = (3)/(2)`

Therefore,
`(3)/(2)` is one of the roots.

2) Next, let's look at (x+5). Write the equation x+5 = 0. Then, isolate x:

`x+5 = 0\\x = -5`

Therefore, -5 is a root as well.

The roots of the equation would be
`(3)/(2)` and -5.