The x-intercepts of a function are the points where the function crosses the x-axis.
The x-intercepts are [tex]\mathbf{ \frac 32, 4, and -3 }[/tex]
The polynomial is given as:
[tex]f(x) = (2x - 3)(x -4)(x + 3)[/tex]
Equate the polynomial to 0
[tex](2x - 3)(x -4)(x + 3) = 0[/tex]
Split the polynomial
[tex]2x - 3 = 0[/tex] or [tex]x -4 = 0[/tex] or [tex]x + 3 = 0[/tex]
Solve for x in all cases
[tex]x = \frac 32[/tex] or [tex]x = 4[/tex] or [tex]x=-3[/tex]
Hence, the x-intercepts are [tex]\mathbf{ \frac 32, 4, and -3 }[/tex]
Read more about intercepts at:
https://brainly.com/question/3334417
