Answer:
Option A.
Step-by-step explanation:
The given function is f(x) = [tex]\frac{2x^{2}+5x-12}{x+4}[/tex]
If denominator of the fraction is zero then the function will be discontinued.
In other words at (x + 4) = 0 the given function will be discontinued.
x = -4 will be the point of discontinuity
Now we will find the factors of numerator to find the zeros of the function.
2x² + 5x - 12 = 2x² + 8x - 3x - 12
= 2x(x + 4) - 3(x + 4)
= (x + 4)(2x - 3)
Now these factors (x + 4) = 0 and (2x -3) are the zero factors of the function.
Therefore, x = [tex]\frac{3}{2}[/tex] will be the zero of the function.
In option A x = -4 is the point of discontinuity and ([tex]\frac{3}{2}[/tex], 0) is the zero of the function.
Option A will be the correct option.
