How do you find the zeros of a function #f(x) = (x^3 + x^2 - 6x) /(4x^2 - 8x - 12)#?
The zeros are
First you have to calculate the domain of the function remembering that 0 cannot be the value of the denominator of a fraction.
So you have to find the solutions of
After dividing both sides by 4 you get
So the domain is
Now you can calculate zeros by solving
So we have just calculated the zeros to be
Now we have to check if the values are in the domain of the function. The calculated zeros are neither -1 or 3 so they all are in the domain and we can finally write the answer:
The zeros of the function are