Answer:
[tex]-\frac{3}{2} , 5[/tex]
Step-by-step explanation:
The zeroes of a function are the x values of the points at which the graph intersects the x-axis. All points on the x-axis have a y-value of 0, therefore, we need to find out which values of x can be plugged in to have the result be 0. This function is already factored out. So, for each expression, find which input of x makes the result equal 0.
1) So, start with 2x + 3. Set it equal to 0 and solve for x:
[tex]2x + 3 = 0\\2x = -3\\x = -\frac{3}{2} \\[/tex]
Therefore, [tex]-\frac{3}{2}[/tex] is one of the zeroes.
2) Next, set x-5 equal to 0 and solve, too:
[tex]x - 5 = 0 \\x = 5 \\[/tex]
Therefore, 5 is one of the zeroes.
3) Thus, the zeroes are [tex]-\frac{3}{2}[/tex] and 5.
